# Math Help - diff eq help

1. ## diff eq help

8y' - 5y = e^((-pi*t)/2), y(0) = a

Let a0 be the value of a for which the transition from one type of behavior to another occurs. The critical value of a0 exactly.

I find that y = (1/8)(e^(-pi/2)) + ce^(-5/8t). I'm lose after that.

2. Originally Posted by lord12
8y' - 5y = e^((-pi*t)/2), y(0) = a

Let a0 be the value of a for which the transition from one type of behavior to another occurs. The critical value of a0 exactly.

I find that y = (1/8)(e^(-pi/2)) + ce^(-5/8t). I'm lose after that.
Solve for C: $C = a - \frac{1}{8}$.

Now I suppose you have to worry about what happens when C = 0, C < 0 and C > 0 .....