Solve :

dy/dx=y³/(e^2x-y²)

Consider dx/dy
dx/dy = (e^2x–y²)/y³
Put e^x=t
gives, e^xdx/dy = dt/dy
So, dt/dy = t³/y³ – t/y
Now, let t=vy
so, dt/dy = v+ydv/dy  
gives, v+ydv/dy=v³-v
therefore, ∫dv/(v³-2v) = ∫dv/v(v+rt2)(v-rt2) = ∫dy/y
Now you can solve it can’t you..
just by partial fractions.