# Solve the Differential Equation y'+Sqrt((1-y^2)/(1-x^2))=0

In this tutorial we shall solve a differential equation of the form $y' + \sqrt {\frac{{1 - {y^2}}}{{1 - {x^2}}}} = 0$, by using separating the variables method.

Given differential equation of the form

This differential equation also be written as

Separating the variables, the given differential equation can be written as

Keep in mind that in separating variable technique the terms $dy$ and $dx$ are placed in the numerator with their respective variables.
Now integration both sides of the equation (i), we have

Using the formula of integration $\int {\frac{1}{{\sqrt {1 - {x^2}} }}dx} = {\sin ^{ - 1}}x + c$, we get

Which is the required solution of the given differential equation.