Solve: `(dy)/(dx)=1/(y^2+siny)`

Answer

`x=frac{y^{3}}{3}-cos y+c`

Explanation

We are given,

`frac{d y}{d x}=\frac{1}{y^{2}+\sin y}`


`\frac{d x}{d y}=y^{2}+\sin y `


Now seperate the variables we get,

`d x=(y^{2}+\sin y) d y`


Integrating both sides,

`int d x=int (y^{2}+\sin y) d y`


`rArr x=\frac{y^{3}}{3}-\cos y+c` , where `c` is the constant term