How to find undetermined coefficients using initial conditions?

Hi, I would like to solve a differential equation something like y=exp(-t)*(c1(cos(w*t)+c2*sin(w*t))).

I have initial conditions as y(0) = 0, and y'(0) = 0.

Using these initial conditions, how can I get the c1 and c2, which are undetermined coefficients? It's pretty straightforward by hand, but it's tricky to code.

Thank you in advance.

[John D'Errico]

Um, that is not a differential equation.

And why is it tricky to code? What have you tried? Show that you are making an effort, and you are more likely to get help. For example, how might you use solve to find the solution?

[ROJO]

I just didn't wanna put a limitation on the methods. I just solved it using subs and solve. Never mind.