Is my solution for the equation (1-x^2)dy/dx -xy = 1/ (1-x^2) correct?

[hotjohn]

Homework Statement

rewrite the equation in the form of linear equation . Then solve it . (1-x^2)dy/dx -xy = 1/ (1-x^2)

the ans given is y= [x/ (1-x^2) ]+ [ C / ( sqrt rt (1-x^2) ) ] , my ans is different , which part is wrong ?

Homework Equations

The Attempt at a Solution

 

[Dr. Courtney]

It can often be useful to plug the given answer back in and verify it is a solution by differentiating and simplifying.

 

[RUber]

$\int (1-x^2)^{-3/2} dx = ...$
Double check that step.
Wolfram Alpha gives: http://www.wolframalpha.com/input/?i=\int+(1-x^2)^{-3/2}+dx

 

[hotjohn]

$\int (1-x^2)^{-3/2} dx = ...$
Double check that step.
Wolfram Alpha gives: http://www.wolframalpha.com/input/?i=\int+(1-x^2)^{-3/2}+dx

why not (1 / (x)(sqrt rt 1-x^2) ) ?

 

[blue_leaf77]

Could you post your calculation with that integral?

 

[RUber]

why not (1 / (x)(sqrt rt 1-x^2) ) ?

What do you get if you take that derivative?
$\frac{d}{dx} x^{-1}(1-x^2)^{-1/2} = -x^{-2}(1-x^2)^{-1/2}+x^{-1}(1-x^2)^{-3/2}\neq (1-x^2)^{-3/2}$