Find the general solution to the linear system $\frac{du}{dt}=Au$ for the following matrices:
a.) $\pmatrix{2&1\\0&2}$
b.) $\pmatrix{-1&-1\\4&-5}$
I got the eigenvalues for a:
$\lambda = 2,2$ repeated roots and the eigenvector, $v_1=\pmatrix{0\\1}$, so the general solution is $c_1e^{2t} + c_2te^{2t}$ but the answer is $\pmatrix{c_1e^{2t}+c_2te^{2t}\\c_2e^{2t}}$. How did they get that?
For b, $\lambda = -3,-3$ and eigenvector, $v_1=\pmatrix{1\\2}$ but the answer is $\pmatrix{c_1e^{-3t}+c_2(\frac{1}{2} +t)e^{-3t}\\2c_1e^{-3t}+2c_2te^{-3t}}$ how did they get that?