# Working backwords from solution to DE

1. Feb 28, 2015

### Panphobia

1. The problem statement, all variables and given/known data
if y = c1*e^t*sin(√3t)+c2*e^t*cos(√3t) + sintcost

3. The attempt at a solution

I have already figured out that (2±√-12)/2 so b = -2 and -12 = 4-4c so c = 4 and a = 1
and that means that the associated homogeneous DE is y'' -2y' + 4y = 0, but I don't know what to do about the sintcost to get then g(t) in y'' -2y' + 4y = g(t), I have tried looking at different methods of solving 2nd order differential equations and tried working backwards but I can't get anything going. What would a good first step be?

2. Feb 28, 2015

### pasmith

$\sin t \cos t = \frac12 \sin(2t)$.

3. Feb 28, 2015

### Panphobia

Yea I got the answer now, thanks a lot!