Solve the following differential equation: `(dy)/(dx)-xsin^2x=1/(xlogx)`

Explanation

`(dy)/(dx)-xsin^2x=1/(xlogx)`


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


Separating variables of equation


`d y=(frac{1}{x log x}+x sin ^{2} x) d x`


Integrating both sides of equation,


`int d y=int(frac{1}{x log x}+x sin ^{2} x) d x` ……. 1


`int frac{1}{x log x} d x`


Let `log x=t`


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