Question

Eigenvalues/Calculus - pic attached

Answer 1

It seemed like my method was right however, i found that there was no solution to the IVP.
Could someone check if the solution has no solution?

Answer 2

I found that the eigenvalues were lamda=1,-2

then i found appropriate eigenvectors for the corresponding eigenvalues.

But when i use the IVP, I find values for C1 and C2

Answer 3

i had as my general solution