Let y=y(x) solve dydx= x+y x( x- x x), x(0,2), y(4)=2.

Question

Let $y=y(x)$ solve $\dfrac{dy}{dx}=\dfrac{	an x+y}{\sin x(\sec x-\sin x	an x)}$, $x\in\left(0,\dfrac{\pi}{2}ight)$, $y\left(\dfrac{\pi}{4}ight)=2$. Then $y\left(\dfrac{\pi}{3}ight)$ is:

Accepted Answer

Simplifying the RHS and solving the resulting linear ODE (dividing through appropriately) gives $y=x\sec x(\dots)$; applying $y(\pi/4)=2$ fixes the constant, and evaluating at $\pi/3$ gives $y=\sqrt3(2+\log_e\sqrt3)$.

Solutions · 1