# Variation of parameters

1. Aug 2, 2005

### EvLer

I have been trying to get this for a while and can't figure it out:

if a fundamental matrix of the system x' = Ax is X(t)
$$\left(\begin{array}{cc}e^t&0\\0&e^{-t}\end{array}\right)$$
find a particular solution yp(t) of $$x' = Ax + [e^t, 2]^{transpose}$$ such that yp(0) = 0

So, I got $$u(t) = \left(\begin{array}{cc}t&0\\0&2e^t\end{array}\right)$$
but when I multiply X(t) by it, I do not get the right answer. Is there a coefficient involved with integration of u'(t)?

Thanks for help.