Hello,

I've just started on separating differential equations and am just having a little trouble on how to proceed with this sort of question.

$\displaystyle \frac {dy}{dx} = y^2 \,e^(2x)$

I understand that the y needs to be bough to the left, and then the formal separation of $\displaystyle \frac {dy}{dx}$ occurs - as my tutor puts it.

$\displaystyle =\frac{1}{y^2}\,dy = e^{2x} dx$

$\displaystyle = \int \frac{1}{y^2}dy = \int e^{2x}$

$\displaystyle = ln\,y^2 = \frac {e^{2x}}{2} + C$

This is where it breaks down a little bit for me...I'd assume that we need to get y to its simplest form, but I don't know how to do that...

$\displaystyle =y^2 = e^{\frac {e^2x}{2}} + C$

That isn't right (I'm assuming), so can someone point me in the direction of the correct step.

Thanks