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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 - Differential Equations - Linear Differential Equation

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

2014-2015 (March)
Question 5.1.2 | 3 marks
Solution for 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 concept: Differential Equations - Linear Differential Equation. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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