# Simple linear differential equation

1. Apr 13, 2010

### raisin_raisin

Hey, I know this is easy I just can't remember how to do it.

$$y(0)=0$$

and $$By''+y'=A$$ A,B constants.

So complementary solution $$Bm^{2}+m=0 \\ \text{ therefore } m=0, \frac{-1}{B}$$
therfore $$y_{C} = C_{1}+C_{2}e^{-t/B}$$
Not sure what to do for particular solution though because substituting in constant doesn't give you anything

$$y= A[t+B(e^{-t/B}-1]$$

Thanks

2. Apr 13, 2010

### LCKurtz

Since y = constant is a solution for the homogeneous equation, it can't be a solution yp of the NH equation. For your particular solution try yp = Ct.

3. Apr 14, 2010

### raisin_raisin

Ah yes now I remember! Thank you very much