Simple linear differential equation

[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

The final answer is:

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

Thanks

 

[LCKurtz]

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

 

[raisin_raisin]

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

Ah yes now I remember! Thank you very much