# Math Help - No idea where to start

1. ## No idea where to start

Solve in general

$\frac{d^2y}{dx^2}+2\frac{dy}{dx}=1+e^{-2x}$

2. Originally Posted by Karl Harder
Solve in general

$\frac{d^2y}{dx^2}+2\frac{dy}{dx}=1+e^{-2x}$
Solve the homogeneous equation first:

$y^{\prime\prime}+2y^{\prime}=0\implies r^2+2r=0\implies r=0$ or $r=-2$.

So we have $y_c=c_1+c_2e^{-2x}$.

Now, we solve the non-homogeneous equation by method of undetermined coefficients.

Take $y_p=Ax+Be^{-2x}+Cxe^{-2x}$, substitute it into the differential equation, and then solve for the unknown coefficients.

Your final answer will be of the form $y=y_c+y_p=\dots$

Can you take it from here?