## Solving second order non homogeneous diff. equation by a particular method

Hi. I have to solve this:

$y''-3y'+2y=e^x$,
Using the replacement $y=\phi y_1$ being $y_1$ a solution of the homogeneous differential equation. I can't do it "traditionally", I have to use this method.

So I have to solve that $\phi ''y_1+ \phi ' \left[2y_1'+Py_1] \right]=e^x$

So, this is what I did:

$y_1=C_1 e^x+C_2e^{2x}\rightarrow y_1'=C_1 e^x+2C_2e^{2x}$
Then:
$\phi ''C_1 e^x+\phi '' C_2 e^{2x}+ \phi ' \left[C_2e^{2x}-C_1e^x \right]=e^x$
What should I do from here? I don't know how to handle $\phi$

Bye there.