#### Question

If y = (tan^{-1} x)^{2}, show that `(1+x^2)^2(d^2y)/dx^2+2x(1+x^2)dy/dx-2=0`

#### Solution

`y=(tan^-1x)^2`

Differentiating w.r.t. x, we get

`dy/dx=2tan^-1x/(1+x^2)`

`(1+x^2)dy/dx=2tan^-1x`

`(1+x^2)(d^2y)/dx^2+2xdy/dx=2/(1+x^2)`

`(1+x^2)^2(d^2y)/dx^2+2x(1+x^2)dy/dx=2`

`(1+x^2)^2(d^2y)/dx^2+2x(1+x^2)dy/dx-2=0`

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#### APPEARS IN

Solution If y = (tan-1 x)2, show that (1+x^2)^2(d^2y)/dx^2+2x(1+x^2)dy/dx-2=0 Concept: Differential Equations - Linear Differential Equation.