Solve the following differential equation: `1/x(dy)/(dx)=tan^(-1)x ,\ x!=0`

Explanation

`frac{1}{x} frac{d y}{d x}=tan ^{-1} x `


`Rightarrow frac{d y}{d x}=x tan ^{-1} x `


`Rightarrow d y=(x tan ^{-1} x) d x`


By Integrating each sides, we obtain



`int d y=int(x tan ^{-1} x) d x `


`Rightarrow int y d y=tan ^{-1} x int x d x-int[frac{d}{d x}(tan ^{-1} x) int x d x] d x `


`Rightarrow y=frac{x^{2} tan ^{-1} x}{2}-frac{1}{2} int frac{x^{2}}{1+x^{2}} d x `


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