HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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Solution for If y = (tan-1 x)2, show that (1+x^2)^2(d^2y)/dx^2+2x(1+x^2)dy/dx-2=0 - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

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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) (with solutions)
Question 5.1.2 | 3.00 marks

Video TutorialsVIEW ALL [1]

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.
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