E&P3 5-3-25
3rd order linear homogeneous IVPPkkkZGVxRzYiLywmLUklZGlmZkclKnByb3RlY3RlZEc2Ji1JInlHRiQ2I0kieEdGJEYuRi5GLiIiJC1GKDYlRitGLkYuIiIjIiIhPkkmaW5pdHNHNiI2JS8tSSJ5R0YkNiMiIiEhIiIvLS1JIkRHRiQ2I0YoRilGKi8tLS1JI0BAR0YkNiRGLyIiI0YwRikiIiI=Pkknc29sZ2VuRzYiLUknZHNvbHZlR0YkNiQ8I0kkZGVxR0YkLUkieUdGJDYjSSJ4R0YkThe exponential rate factors come fromLUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy8sJiokSSJyR0YnIiIkRi0qJEYsIiIjRi8iIiE=The one repeated root leads to the linear expression multiplying 1.
How does Maple get the IVP solution from the general solution?Pkknc29saXZwRzYiLUknZHNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQ8JEkkZGVxR0YkSSZpbml0c0dGJC1JInlHRiQ2I0kieEdGJA==We evaluate the linear system of conditions and then solve that linear system either with the inverse matrix or by row reductionPkkiWUc2ImYqNiNJInhHRiRGJDYkSSlvcGVyYXRvckdGJEkmYXJyb3dHRiRGJCwoSSRfQzFHRiQiIiIqJkkkX0MyR0YkRi05JEYtRi0qJkkkX0MzR0YkRi0tSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkRjAjISIjIiIkRi1GLUYkRiRGJA==QyU2JS8tSSJZRzYiNiMiIiEhIiIvLUklZXZhbEclKnByb3RlY3RlZEc2JC1JJWRpZmZHRi42JC1GJjYjSSJ4R0YnRjUvRjVGKUYpLy1GLTYkLUYxNiVGM0Y1RjVGNiIiIkY8LUkmc29sdmVHNiRGLkkoX3N5c2xpYkdGJzYkPCNJIiVHRic8JUkkX0MxR0YnSSRfQzJHRidJJF9DM0dGJw=="By Hand."
The matrix solution of the initial conditions goes via the augmented matrix:LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNSFmPV1PdVN1WSU9QyUtX0kuTGluZWFyQWxnZWJyYUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ikk2UmVkdWNlZFJvd0VjaGVsb25Gb3JtR0YpNiMtSSdNYXRyaXhHRiY2Iy9JJCVpZEdGKSI1IWY9XU91U3VZJT0iIiIvLSZJJ1ZlY3RvckdGJjYjSSdjb2x1bW5HRik2Iy9GMCI1QXcnXE91U3VZJT0tJkYlNiNJM0JhY2t3YXJkU3Vic3RpdHV0ZUdGKTYjSSIlR0Ypor by the inverse matrix:QyQtSSV3aXRoRzYiNiNJLkxpbmVhckFsZ2VicmFHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUhIiI=QyU+SSJBRzYiLUktRGVsZXRlQ29sdW1uR0YlNiQtSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2Iy9JJCVpZEdGJSI1NTxeW1YyV25XPSIiJSIiIj5JImJHRiUtRic2JEYpO0YzIiIkLy0mSSdWZWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0knY29sdW1uR0YpNiMvSSQlaWRHRikiNTVOXltWMlduVz0tSTBkZWxheURvdFByb2R1Y3RHNiRGJy9JK21vZHVsZW5hbWVHRilJLFR5cGVzZXR0aW5nR0YmNiUqJEkiQUdGKSEiIkkiYkdGKUkldHJ1ZUdGJw==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzQwMDczNzEwWCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjLSIkIiUmJSJtRzYkIiIiRikmRic2JCIiI0YpJkYnNiQiIiRGKSZGJzYkRilGLCZGJzYkRixGLCZGJzYkRi9GLCZGJzYkRilGLyZGJzYkRixGLyZGJzYkRi9GLyZGJzYkRikiIiUmRic2JEYsRj4mRic2JEYvRj5GJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzY1MDA5NjYyWColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkJiUibUc2JCIiIkYpJkYnNiQiIiNGKSZGJzYkIiIkRilGJQ==