Question

Find the general solution of the differential equation

Answer 1

The differential equation is dy dx + 1− y 2 1− x 2 =0.

Simplify the above equation.

dy dx + 1− y 2 1− x 2 =0 dy dx =− 1− y 2 1− x 2 dy 1− y 2 = −dx 1− x 2

Integrate the both sides of above equation.

sin −1 y=− sin −1 x+C sin −1 x+ sin −1 y=C

Therefore, the general solution of differential equation is sin −1 x+ sin −1 y=C.