Let y=y(x) solve ^2x,dy+2,dx=(1+y2x)^2x,dx, y(4)=0.

Question

Let $y=y(x)$ solve $\csc^2x\,dy+2\,dx=(1+y\cos2x)\csc^2x\,dx$, $y\left(\dfrac{\pi}{4}\right)=0$. Then $(y(0)+1)^2$ is:

Accepted Answer

$$\frac{dy}{dx}-(\cos2x)y = \cos2x.$$

I.F.$=e^{-\sin2x/2}$; solving with $y(\pi/4)=0$ gives $y(0)=-1+e^{-1/2}$, so $(y(0)+1)^2=e^{-1}$.

Solutions · 1