Question

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

Answer 1

`y=2√(\sin \left(x\right)-1),\:y=-2√(\sin \left(x\right)-1)`

Step-by-step explanation:

`(dy)/(dx)=(\cos \left(x\right))/(y)2`

`y'\:=(\cos \left(x\right))/(y)\cdot \:2`

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

`yy'\:=2\cos \left(x\right):\quad (y^2)/(2)=2\sin \left(x\right)+c_1`

`(y^2)/(2)=2\sin \left(x\right)-2`

`y=2√(\sin \left(x\right)-1),\:y=-2√(\sin \left(x\right)-1)`