# Convolution and a diff eq

1. Sep 30, 2006

### tandoorichicken

Any hints to this problem?

"Assume the solution to a differential equation is given by
$$\frac{dy(x)}{dx}+ay(x) = f(x)$$
where $y(0)=y_0$ and a is a constant. Show how y(x) can be written as a convolution of f(x) and an exponential $e^{ax}$."

The only hint we got from the prof was to multiply both sides by the exponential and express the left as a single term, but I could be doing something wrong there as well. Anyone have any more hints? (I don't want the solution just yet, I just want to try to work it out first)

Thanks

2. Oct 1, 2006

### doodle

Upon multiplying both sides with the exponential, recall next that
$$\frac{d(uv)}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$$