Hey, I'm not sure how to start this problem, as the ODE does not seem to be seperable. (We have only had 1 lecture on seperable equations / exponential models).

I feel blind.

I think that I need to seperate the equation to the form $\displaystyle f(y)dy=g(x)dx$ and integrate, but I cannot figure out how to obtain that. Once I do, I think we sub in $\displaystyle y=e^{2x}sinx$ into the integrated equation and hit $\displaystyle x=0$ to show that the result is $\displaystyle 0=0$.Verify that the function $\displaystyle y=e^{2x}sin(x)$ is a solution of the Initial Value Problem $\displaystyle \frac{dy}{dx}sin(x) -ycos(x) = e^{2x}sin^2x, \ \ y(0)=0$.

Am I on the right track?