The solution of differential equation
`(1+x^(2)) (dy)/(dx) + y = e^(tan^(-1)x)`

Explanation

``
`(1+x^{2}) frac{d y}{d x}+y=e^{tan ^{-1} x} `


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


``
The above `{DE}` is of the form `frac{{dy}}{{dx}}+{P}_{{y}}=Q`


Integrating factor (I.F) `=e^{int p d x}`


``
`=e^{int frac{1}{1+x^{2}} d x}{because(tan ^{-1} x)^{1}=frac{1}{1+x^{2}}} `


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