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If y=(tan^(-1)x)^2, show that (x^2+1)^2y...

If `y=(tan^(-1)x)^2`, show that `(x^2+1)^2y_2+2x(x^2+1)y_1=2`

Text Solution

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`y= (tan^(-1)x)^(2)`
`=(dy)/(dx)=2tan^(-1)x*(1)/(1+x^(2))`
`implies (1+x^(2))(dy)/(dx)=2tan^(-1)x`
Again, differentiate both sides w.r.t. x
`(1+x^(2))(d^(2)y)/(dx^(2))+2x(dy)/(dx)=(2)/(1+x^(2))`
`implies(1+x^(2))^(2)(d^(2)y)/(dx^(2))+2x(1+x^(2))(dy)/(dx)=2`
`implies(1+x^(2))^(2)(d^(2)y)/(dx^(2))+2x(1+x^(2))(dy)/(dx)-2=0 " "`Hence Proved.
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