Solve the differential equation`(dy)/(dx)+sqrt((1-y^2)/(1-x^2))=0`

Answer

`sin^(-1) y+sin^(-1) x=c`

Explanation

We are given

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


`rArr (dy)/(dx)=-sqrt((1-y^2)/(1-x^2))`


Separating the variables we get,

`rArr (dy)/sqrt(1-y^2)=-dx/sqrt(1-x^2)`


Integrating both sides we get,

`int (dy)/sqrt(1-y^2)=-int dx/sqrt(1-x^2)`


We have the direct formula for this `int (dy)/sqrt(1-y^2)=sin^(-1) y`

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