# Math Help - non-homogeneous equation

1. ## non-homogeneous equation

1.) (D^2+1)=cosx

2.) y"-3y'-4y=16x-50cos2x

2. Originally Posted by alderon
1.) (D^2+1)=cosx

2.) y"-3y'-4y=16x-50cos2x
The general solutions to these take the form of the general solution to the corresponding homogeneous equation plus a particular integral of the non homogeneous equation.

I will presume that you know how to solve the homogeneous equations $y''+y=0$ (which is what I presume your first equation id supposed to be) and $y''-3y'-4y=0$

For the first, as $\cos(x)$ is a solution of the homogeneous equation we try a trial solution $(Ax+B)\cos(x) + (Cx+D)\sin(x)$

For the second we try a trial solution of the form $(A x+ B) + C \cos(2x)+D \sin(2x)$

RonL