EPC4 5.5.4 find the particular solution of 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.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 the particular solution 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 we derive this.
There is no root overlap between the LHS and the RHS so we can just take a general linear coefficient times this exponential as our trial functionLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEoJm1pbnVzO0YnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGWC1GOzYkUSI4RidGPi1GRDYtUSJ+RidGPkZHRkpGTEZORlBGUkZUL0ZXUSYwLjBlbUYnL0ZaRlxvRi4tRkQ2LVEiK0YnRj5GR0ZKRkxGTkZQRlJGVEZWRlktRjs2JFEiNUYnRj4tRkQ2LVEiPUYnRj5GR0ZKRkxGTkZQRlJGVC9GV1EsMC4yNzc3Nzc4ZW1GJy9GWkZoby1GOzYkRkJGPi1GRDYtUSI7RidGPkZHL0ZLRjRGTEZORlBGUkZURltvRmlvLUYvNiVRJnNvbHZlRidGMkY1LUkobWZlbmNlZEdGJDYkLUYjNiUtRi82JVEiJUYnRjJGNS8lK2V4ZWN1dGFibGVHRklGPkY+RltxRj4=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSI9RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUY2NiQtRiM2KC1GLDYlUSNjM0YnRi9GMi1GQDYtUSIrRidGPUZDRkZGSEZKRkxGTkZQL0ZTUSwwLjIyMjIyMjJlbUYnL0ZWRlxvLUYsNiVRI2M0RidGL0YyLUZANi1RIn5GJ0Y9RkNGRkZIRkpGTEZORlAvRlNRJjAuMGVtRicvRlZGZW9GOkY9Rj1GYW8tSSVtc3VwR0YkNiUtRkA2LVEvJkV4cG9uZW50aWFsRTtGJ0Y9L0ZEUSZ1bnNldEYnL0ZHRl5wL0ZJRl5wL0ZLRl5wL0ZNRl5wL0ZPRl5wL0ZRRl5wRmRvL0ZWUSwwLjExMTExMTFlbUYnLUYjNiVGYW9GOkY9LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHRkVGPQ==now we backsubstitute term by term and add them together and equate to the coefficient of the common exponential on the RHS.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 the Maple result.