Verify that the given vector is the general solution of the corresponding homogeneous system and then solve the nonhomogenous system. Assume that t>0.
|2 -1|x + |1- t^2|
|3 -2| |2t |
c1| 1|t + c2| 1|t^-1
| 1| |3|
This won't show up correctly but the first eigen vector is (1,1) and the second is (1,3)
The Attempt at a Solution
So I have been solving non homogeneous linear systems all night with no problems however when I got to this problem I got stumped because there is a t in front of x'. I solved for the eigen values and eigen vectors and the eigen vectors match what they have but I have the general solution by solving it without acknowledging the t in front of x'. I thought that maybe I could just divide my general solution I got by t and then I would have the same answer, however that doesn't work because the solution provided by the problem doesn't have any e^t's in it. So I am not quite sure on what is going on exactly.