1. ## Basic Differential Equation

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.

Verify that the function $\displaystyle y=e^{2x}sin(x)$ is a solution of the Initial Value Problem $\displaystyle \frac{dy}{dx}sin(x) -ycos(x) = e^{2x}sin^2x, \ \ y(0)=0$.
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 $\displaystyle 0=0$.

Am I on the right track?

2. oh, don't over complicate this, check the solution, that's all, you need to put it into the ODE and you'll see it verifies the equality.

3. Originally Posted by Krizalid
oh, don't over complicate this, check the solution, that's all, you need to put it into the ODE and you'll see it verifies the equality.
Jeeeez. Over-complicating indeed, thanks man!