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If y = (tan-1 x)2, show that (1+x^2)^2(d^2y)/dx^2+2x(1+x^2)dy/dx-2=0 - Mathematics and Statistics

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Sum

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

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

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Solution

y = tan -1

y1 = `1/(1+"x"^2)`

y2 = `(d(1+x^2)^(-1))/"dx" = -1/(1+x^2)^2 xx ("2x")`

y2 = `(-2x)/(1+x^2)^2`

y2 (1+x2) = -2x `(1/(1+x^2))`

y2 (1+x2) = -2 xy1 

y2 (1+x2) + 2xy1 = 0

Concept: Differential Equations - Linear Differential Equation
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