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Solve the equation (1-x^2)((dy)/(dx))+2x...

Solve the equation `(1-x^2)((dy)/(dx))+2x y=xsqrt(1-x^2)`

Text Solution

Verified by Experts

The correct Answer is:
`y=sqrt(1-x^(2))+c(1-x^(2))`
We have
`(dy)/(dx)+(2x)/(1-x^(2))y=x/sqrt(1-x^(2))`
Here, `P=(2x)/(1-x^(2))` and `q=x/sqrt(1-x^(2))`
`I.F. e^(int(2x)/(1-x^(2))dx)=e^(-log(1-x^(2)))=1/(1-x^(2))`
Therefore, the solution is
`y/(1-x^(2))=int(x)/sqrt((1-x^(2)) xx 1/(1-x^(2))dx+c`
`=1/sqrt(1-x^(2))+c`
or `y=sqrt(1-x^(2))+c(1-x^(2))`
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