Solve the following differential equations: `(dy)/(dx)+(4x)/(x^2+1)y+1/((x^2+1)^2)=0`

Explanation

`frac{d y}{d x}+frac{4 x}{x^{2}+1} y=frac{1}{(x^{2}+1)^{3}} quad ldots(1)`


Here `P=frac{4 x}{x^{2}+1} Rightarrow int {P} d {x}=int frac{4 {x}}{{x}^{2}+1} {dx}=2 log ({x}^{2}+1)=log ({x}^{2}+1)^{2}`
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therefore { I.F. }={e}^{log ({x}^{2}+1)^{2}}=({x}^{2}+1)^{2}`


Multiplying (1) by I.F. we get
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