MAT2705-03/04 11F Quiz 8 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use arrows and equal signs when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC).
1. 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 ,
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 .a) Rewrite this system of DEs and its initial conditions explicitly in matrix form for the vector variable LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JUYrLUkmbW92ZXJHRiQ2JS1GLDYnUSJ4RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y5LyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GIzYkLUkjbW9HRiQ2LVEuJlJpZ2h0VmVjdG9yO0YnL0Y9USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTC8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0ZMLyUobGFyZ2VvcEdGTC8lLm1vdmFibGVsaW1pdHNHRkwvJSdhY2NlbnRHRkwvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZlbkZIRldGSC1GRTYtUSI9RidGSEZKRk0vRlBGTEZRRlNGVUZXRllGZm4tSShtZmVuY2VkR0YkNiYtRiM2KC1JJW1zdWJHRiQ2JS1GLDYlRjZGOi9GPVEnaXRhbGljRictRiM2JC1JI21uR0YkNiRRIjFGJ0ZIRkgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GRTYtUSIsRidGSEZKL0ZORjlGW29GUUZTRlVGVy9GWlEmMC4wZW1GJy9GZ25RLDAuMzMzMzMzM2VtRictRmJvNiVGZG8tRiM2JC1GW3A2JFEiMkYnRkhGSEZecEZhcC1GYm82JUZkby1GIzYlLUZbcDYkUSIzRidGSEY6RmZvRl5wRkhGSC8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RidGSA== as a column matrix (using the actual matrices, not their symbols), identifying the coefficient matrix A.b) For this LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, using Maple write down the eigenvalues 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 and corresponding matrix of eigenvectors LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiNRIUYnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw== =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 that it provides you.c) Pick one eigenvector 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 and evaluate by hand the product 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 and compare with 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 . Do they agree?d) Use technology to evaluate and write down the inverse matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlEtSSNtbkdGJDYkUSIxRidGPkYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYvNiNRIUYnRj4= and use Maple to evaluate the matrix product 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. Write down this result. Does it evaluate correctly to the diagonalized matrix with the eigenvalues in the correct order?e) Given that 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, if 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 , find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRInlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUS0mUmlnaHRBcnJvdztGJy8lLHBsYWNlaG9sZGVyR0Y0L0Y2USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRL0ZORjQtSShtZmVuY2VkR0YkNiQtRiM2JC1JI21uR0YkNiRRIjBGJ0Y+Rj5GPkY+ . Show how you did this.f) Express the new components of the system of differential equations: 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, solve them, then backsubsitute into 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.
g) Impose the initial conditions and express your solution for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1GIzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GOFEnbm9ybWFsRictSSNtb0dGJDYuUS0mUmlnaHRBcnJvdztGJy8lLHBsYWNlaG9sZGVyR0Y2RjovJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUy9GUEY2Rjo= both in matrix form, multiplying out to obtain the scalar solutions for the individual unknowns, as well as in the linear combination vector form which shows the three modes, and then combine the two modes associated with the repeated eigenvalue to get a linear combination of only 2 independent vectors.h) The resulting motion takes place in a plane. State a basis for that plane.
i) What are the two characteristic times for the exponential decays? Plot your solutions for 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 where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is 5 times the larger characteristic time. Make a rough sketch of what you see, labeling the three curves by their variables, and labeling the axes with tickmarks and the norizontal one with its variable name. Two of the curves merge in your plot. Their difference decays with the smaller characteristic time constant. Does the interval over which they merge roughly agree with 5 times that smaller time constant?j) Only one of these curves has a local extremum. Find its coordinates exactly and approximately to 3 significant digits. Is your result consistent with your plot? solution1.a)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkobWZlbmNlZEdGJDYmLUYjNjAtSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYkUSIxRicvRjtRJ25vcm1hbEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRidGQy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiJ0YnRkMvJSZmZW5jZUdGRy8lKnNlcGFyYXRvckdGRy8lKXN0cmV0Y2h5R0ZHLyUqc3ltbWV0cmljR0ZHLyUobGFyZ2VvcEdGRy8lLm1vdmFibGVsaW1pdHNHRkcvJSdhY2NlbnRHRkcvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR1EmMC4wZW1GJy1GLDYkLUYjNiYtRjQ2JVEidEYnRjdGOkZFRkhGQ0ZDLUZPNi1RIixGJ0ZDRlIvRlVGOUZWRlhGWkZmbkZobi9GW29GX28vRl5vUSwwLjMzMzMzMzNlbUYnLUYxNiVGMy1GIzYmLUZANiRRIjJGJ0ZDRkVGSEZDRktGTkZgb0Znby1GMTYlRjMtRiM2Ji1GQDYkUSIzRidGQ0ZFRkhGQ0ZLRk5GYG9GRUZIRkNGQy8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RictRk82LVEiPUYnRkNGUkZURlZGWEZaRmZuRmhuL0Zbb1EsMC4yNzc3Nzc4ZW1GJy9GXm9GZnEtSShtYWN0aW9uR0YkNiQtRiM2Ji1GNDYjUSFGJy1GaXE2JC1GIzYmLUZpcTYkLUYsNigtRiM2JkZdci1JJ210YWJsZUdGJDY3LUkkbXRyR0YkNigtSSRtdGRHRiQ2KC1GIzYlLUZPNi1RKiZ1bWludXMwO0YnRkNGUkZURlZGWEZaRmZuRmhuL0Zbb1EsMC4yMjIyMjIyZW1GJy9GXm9GaXNGYnBGQy8lKXJvd2FsaWduR0Zfci8lLGNvbHVtbmFsaWduR0Zfci8lK2dyb3VwYWxpZ25HRl9yLyUocm93c3BhbkdGQi8lK2NvbHVtbnNwYW5HRkItRmFzNigtRiM2JC1GQDYkRk1GQ0ZDRlt0Rl10Rl90RmF0RmN0RmV0Rlt0Rl10Rl90LUZeczYoLUZhczYoLUYjNiQtRkA2JFEiN0YnRkNGQ0ZbdEZddEZfdEZhdEZjdC1GYXM2KC1GIzYlRmVzLUZANiRRIjlGJ0ZDRkNGW3RGXXRGX3RGYXRGY3QtRmFzNigtRiM2JUZlc0ZhdUZDRlt0Rl10Rl90RmF0RmN0Rlt0Rl10Rl90LUZeczYoRmV0RmV0RmBzRlt0Rl10Rl90LyUmYWxpZ25HUSVheGlzRicvRlx0USliYXNlbGluZUYnL0ZedFEnY2VudGVyRicvRmB0USd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGOS8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRl53LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRml3LyUmZnJhbWVHRml3LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGRy8lLWVxdWFsY29sdW1uc0dGRy8lLWRpc3BsYXlzdHlsZUdGRy8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0Zmd0ZdckZDRkMvSSttc2VtYW50aWNzR0YkUSdNYXRyaXhGJy9GXXFRIltGJy9GYHFRIl1GJ0ZceS8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRidGXXJGQ0ZceUZjeUZdckZDRmN5LUZPNi1RIn5GJ0ZDRlJGVEZWRlhGWkZmbkZobkZbcEZdby1GLDYmLUYjNistRjE2JUYzLUYjNiRGP0ZDRkstRiw2JC1GIzYkRmRvRkNGQ0Znby1GMTYlRjMtRiM2JEZicEZDRktGYXpGZ28tRjE2JUYzLUYjNiRGaXBGQ0ZLRmF6RkNGQ0ZccUZfcUZdckZFRkM=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSV3aXRoRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEoU3R1ZGVudEYnRi9GMi1GUzYmLUYjNiUtRiw2JVEuTGluZWFyQWxnZWJyYUYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRltvRjlGOUY1RltvRjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWFjdGlvbkdGJDYkLUYjNictRiw2I1EhRictRlA2JC1JKG1mZW5jZWRHRiQ2KC1GIzYmRlQtSSdtdGFibGVHRiQ2Ny1JJG10ckdGJDYoLUkkbXRkR0YkNigtRiM2JS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GZ28tSSNtbkdGJDYkUSIyRidGOUY5LyUpcm93YWxpZ25HRlYvJSxjb2x1bW5hbGlnbkdGVi8lK2dyb3VwYWxpZ25HRlYvJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGZXAtRl9vNigtRiM2JC1Gam82JFEiMEYnRjlGOUZdcEZfcEZhcEZjcEZmcEZocEZdcEZfcEZhcC1GXG82KC1GX282KC1GIzYkLUZqbzYkUSI3RidGOUY5Rl1wRl9wRmFwRmNwRmZwLUZfbzYoLUYjNiVGY28tRmpvNiRRIjlGJ0Y5RjlGXXBGX3BGYXBGY3BGZnAtRl9vNigtRiM2JUZjb0ZlcUY5Rl1wRl9wRmFwRmNwRmZwRl1wRl9wRmFwLUZcbzYoRmhwRmhwRl5vRl1wRl9wRmFwLyUmYWxpZ25HUSVheGlzRicvRl5wUSliYXNlbGluZUYnL0ZgcFEnY2VudGVyRicvRmJwUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGMS8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmJzLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRl10LyUmZnJhbWVHRl10LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGPS8lLWVxdWFsY29sdW1uc0dGPS8lLWRpc3BsYXlzdHlsZUdGPS8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0Zqc0ZURjlGOS9JK21zZW1hbnRpY3NHRiRRJ01hdHJpeEYnLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmB1LyUrYWN0aW9udHlwZUdRLnJ0YWJsZWFkZHJlc3NGJ0ZURi9GMkZpdUZULyUrZXhlY3V0YWJsZUdGPUY5b)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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUklbXN1YkdGJDYlRistRiM2Iy1GLDYlUSZtYXBsZUYnRi9GMi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnc) The matrix 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 =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 is clearly LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlEtSSNtbkdGJDYkUSIxRidGPi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRic=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
e) The new coordinates of the given point are 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 is also the solution of the initial conditions for the arbitrary constants below.f),g) Therefore the solution is this linear combination of the products of the exponentials with eigenvalues as rate factors times the corresponding eigenvectors:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRLkxpbmVhckFsZ2VicmFGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiOkYnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVA==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The decoupled equations 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Their obvious solutions are the exponentials with eigenvalue rate factors. 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h) Maple's direct solution:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZaLUkjbWlHRiQ2JVEjeDFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSInRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEidEYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjc3Nzc3OGVtRicvRk5GaG4tRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORl5vLUkjbW5HRiQ2JFEiMkYnRjktRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSC9GS0ZPRk1GK0ZQLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGZ28vRk5RLDAuMzMzMzMzM2VtRictRiw2JVEjeDJGJ0YvRjJGNUZQRlotRmFvNiRRIjdGJ0Y5RmRvRitGUC1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRl1vRl9vLUZhbzYkUSI5RidGOUZkb0ZecEZQRmRwRmFwRmRvLUYsNiVRI3gzRidGL0YyRlBGaG9GanBGNUZQRlpGam5GYG9GZG9GanBGUEZob0YrLUZRNiQtRiM2JS1GYW82JFEiMEYnRjlGWEY5RjlGWkZgb0Zob0ZecEZdcUZaRmpuRmBvRmhvRmpwRl1xRlotRmFvNiRRIjFGJ0Y5RlhGOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEkc29sRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJWJvbGRHUSZmYWxzZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYwUSomY29sb25lcTtGJ0YvRjJGOC9GPFEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUYsNihRJ2Rzb2x2ZUYnRi9GMkY1RjhGOy1JKG1mZW5jZWRHRiQ2KS1GIzYmLUY/NjBRIidGJ0YvRjJGOEZCRkRGRkZIRkpGTEZORlAvRlNRLDAuMTExMTExMWVtRicvRlZRJjAuMGVtRictRj82MFEjOi1GJ0YvRjJGOEZCRkRGRkZIRkpGTEZORlAvRlNGX29GXm8tRiw2KFEsaW50ZXJhY3RpdmVGJ0YvRjJGNUY4RjtGaW5GL0YyRjhGQi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GZW42Jy1GIzYlLUY/NjBRIn5GJ0YvRjJGOEZCRkRGRkZIRkpGTEZORlBGY29GXm8tRmVuNiktRiM2JS1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWJhbDYoLy0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJI3gxRzYiNiNJInRHNiIsJComIiIjIiIiLUkjeDFHNiI2I0kidEc2IiIiIiEiIi8tLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSN4Mkc2IjYjSSJ0RzYiLCgqJiIiKCIiIi1JI3gxRzYiNiNJInRHNiIiIiIiIiIqJiIiKiIiIi1JI3gyRzYiNiNJInRHNiIiIiIhIiIqJiIiKCIiIi1JI3gzRzYiNiNJInRHNiIiIiIhIiIvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kjeDNHNiI2I0kidEc2IiwkKiYiIiMiIiItSSN4M0c2IjYjSSJ0RzYiIiIiISIiLy1JI3gxRzYiNiMiIiEiIiMvLUkjeDJHNiI2IyIiISEiIy8tSSN4M0c2IjYjIiIhIiIiRicvJSthY3Rpb250eXBlR1E6bWFwbGVzb2Z0LmNvbTpsYWJlbChMMzU5KUYnLyUldmlld0dRJmxhYmVsRidGaHBGL0YyRjhGQi9GaG9RInxmckYnL0ZbcFEifGhyRictRj82MUZjcEYvRjJGOC8lK2V4ZWN1dGFibGVHRjRGQkZERkZGSEZKRkxGTkZQRmNvRl5vRi9GMkY4RkI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJHNvbEYnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjY2Ji1GIzYqLUYsNiVRI3gxRidGL0YyLUY2NiQtRiM2Iy1GLDYlUSJ0RidGL0YyRkFGPS1GLDYlUSN4MkYnRi9GMkZpbkY9LUYsNiVRI3gzRidGL0YyRmluRkEvJSVvcGVuR1EnJmxhbmc7RicvJSZjbG9zZUdRJyZyYW5nO0YnRkE=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUklbXN1cEdGJDYlLUkjbW9HRiQ2LVEvJkV4cG9uZW50aWFsRTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTExMTExMWVtRictRiM2Ji1GLzYtUSomdW1pbnVzMDtGJ0YyRjVGOEY6RjxGPkZARkIvRkVRLDAuMjIyMjIyMmVtRicvRkhGUC1JI21uR0YkNiRRIjJGJ0YyLUYvNi1RIn5GJ0YyRjVGOEY6RjxGPkZARkJGRC9GSEZGLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGVi1GLzYtUSI8RidGMkY1RjhGOkY8Rj5GQEZCL0ZFUSwwLjI3Nzc3NzhlbUYnL0ZIRmRvRlItRi82LVEiLEYnRjJGNS9GOUZqbkY6RjxGPkZARkJGRC9GSFEsMC4zMzMzMzMzZW1GJy1GUzYkUSIxRidGMkZmb0ZccC1GLzYtUSI+RidGMkY1RjhGOkY8Rj5GQEZCRmNvRmVvRkwtRlM2JFEiM0YnRjJGVi1GLDYlRi4tRiM2JkZMLUZTNiRRIjlGJ0YyRlZGWkZdb0ZWLUkobWZlbmNlZEdGJDYmLUYjNictRlM2JEZfb0YyRmZvRlxwRmZvRmFxRjIvJSVvcGVuR1EnJmxhbmc7RicvJSZjbG9zZUdRJyZyYW5nO0Yni) The characteristic times are 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 or LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JFEkMC41RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjM2LVEifkYnRi9GNi9GOkY4RjxGPkZARkJGREZGL0ZKRkgtRiw2JFEmMC4xMTFGJ0YvRi8=. The appropriate window is therefore 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iM1Z1WkVkUkxsc3lOVFVzTWpVMUxESTFOVjFHSnk4bEoyOXdZWEYxWlVkR09pOGxLMlY0WldOMWRHRmliR1ZIUmpvdkpTbHlaV0ZrYjI1c2VVZEdPaThsS1dOdmJYQnZjMlZrUjBZNkx5VXFZMjl1ZG1WeWRHVmtSMFk2THlVcmFXMXpaV3hsWTNSbFpFZEdPaThsTEhCc1lXTmxhRzlzWkdWeVIwWTZMeVUyYzJWc1pXTjBhVzl1TFhCc1lXTmxhRzlzWkdWeVIwWTZMeVVzYldGMGFIWmhjbWxoYm5SSFVTZHBkR0ZzYVdOR0p5MUdJelkxTFVramJXNUhSaVEyTlZFaU0wWW5SakpHTlVZNEwwWThSanBHUGtaQVJrSkdSRVpIUmtwR1RFWk9SbEJHVWtaVVJsWkdXQzlHWlc1UkoyNXZjbTFoYkVZblJqSkdOVVk0Ump0R1BrWkFSa0pHUkVaSFJrcEdURVpPUmxCR1VrWlVSbFpHV0VaYUx5VXZjM1ZpYzJOeWFYQjBjMmhwWm5SSFVTSXdSaWRHVmtZeUwwWTJVU014TWtZblJqaEdYVzlHUGtaQVJrSkdSRVpIUmtwR1RFWk9SbEJHVWtaVVJsWkdXRVplYnc9PTwvRXF1YXRpb24+PC9UZXh0LWZpZWxkPg==6"Yes, the last two variables (blue and green curves) merge at about this time:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Iy1GLzYkUSM5LkYnRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRj8vJSliZXZlbGxlZEdRJmZhbHNlRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjWDFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSN0MUYnRi9GMi9GM1Enbm9ybWFsRic=A bit ugly because of the rationaiization of the denominator.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoaWZhY3RvckYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUkjbW5HRiQ2JFEkMjQzRicvRjNRJ25vcm1hbEYnRj4=Solving by hand gives the simplest form of this radical:LCQtSSJeRyUqcHJvdGVjdGVkRzYkIyIiIyIjRiNGKCIiKCNGKyIiKg==JSFHThe local max (= global max) of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ occurs at 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 where 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TTdSMApJNlJUQUJMRV9TQVZFLzQ1MTUyOTI2NFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyoiJCIkISIjIiIoIiIhRikhIipGKUYpISIoRidGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzM5MTQzMlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCEiI0YnISIqRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzQ1NjU3NlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyoiJCIkIiIiIiIhRidGJ0YnRihGKEYnRihGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzQ1NjU3NlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyoiJCIkIiIiIiIhRidGJ0YnRihGKEYnRihGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzQ1NjcyOFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyoiJCIkISIjIiIhRidGJ0YnRihGKCEiKkYoRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzQ1Njg4MFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyoiJCIkIiIhIiIiISIiRidGJ0YoRihGKUYoRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzQ4OTcxMlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyoiJCIkISIjIiIhRihGKEYnRihGKEYoISIqRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzQ4OTg2NFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCIiIkYnISIkRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzQ5MDAwMFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCwkLSUkZXhwRzYjLCQlInRHISIjIiIjLCZGKCIiIi1GKTYjLCRGLCEiKiEiJEYoRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzUzNTA3MlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJC0tJSJERzYjJiUieUc2IyIiIjYjJSJ0Ry0tRik2IyZGLDYjIiIjRi8tLUYpNiMmRiw2IyIiJEYvRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzcwMjI4MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCwkLSYlInlHNiMiIiI2IyUidEchIiMsJC0mRio2IyIiI0YtRi8sJC0mRio2IyIiJEYtISIqRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzcwMjQxNlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCwmKiYmJSJjRzYjIiIiRiwtJSRleHBHNiMsJCUidEchIiNGLEYsKiYmRio2IyIiI0YsRi1GLEYsLCZGM0YsKiYmRio2IyIiJEYsLUYuNiMsJEYxISIqRixGLEYoRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzczNTIwOFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCwmKiYmJSJjRzYjIiIiRiwtJSRleHBHNiMsJCUidEchIiNGLEYsKiYmRio2IyIiI0YsRi1GLEYsLCZGM0YsKiYmRio2IyIiJEYsLUYuNiMsJEYxISIqRixGLEYoRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzczNTM0NFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCwkLSUkZXhwRzYjLCQlInRHISIjIiIjLCZGKCIiIi1GKTYjLCRGLCEiKiEiJEYoRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1Mzc2ODI1NlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCwkLSUkZXhwRzYjLCQlInRHISIjIiIjLCZGKCIiIi1GKTYjLCRGLCEiKiEiJEYoRiU=