Solving IVP: Is My Answer Correct?

[squenshl]

I had to solve an IVP:
$$\partial$$/$$u\partial$$t + 4$$\partial$$u/$$\partial$$x = e^2x, u(x,0) = f(x).
I got an answer of u = 1/2 +f(x-4t).
Is this correct and if not, where did I go wrong.

 

[LCKurtz]

Hard to tell where you went wrong without seeing your work. But it isn't correct for at least two reasons:

1. It doesn't satisfy u(x,0) = f(x) (although it would without the 1/2).
2. If you plug it into the DE you get 0, not e^(2x).