Question

Find the solution to the differential equation dy/dx = cos(x) / y2 , where y(π/2) = 0.

Answer 1

Answer:

$y=2\sqrt{\sin \left(x\right)-1},\:y=-2\sqrt{\sin \left(x\right)-1}$

Explanation:

$\frac{dy}{dx}=\frac{\cos \left(x\right)}{y}2$

$y'\:=\frac{\cos \left(x\right)}{y}\cdot \:2$

$yy'\:=2\cos \left(x\right)$

$yy'\:=2\cos \left(x\right):\quad \frac{y^2}{2}=2\sin \left(x\right)+c_1$

$\frac{y^2}{2}=2\sin \left(x\right)-2$

$y=2\sqrt{\sin \left(x\right)-1},\:y=-2\sqrt{\sin \left(x\right)-1}$