Solve the following differential equations:

Now separating variable x on one side and variable y on another side, we have,

Let 1 – x² = t² and 1 – y² = t²

Differentiating we get

xdx = – tdt

ydy = – vdv

substituting these values in above differential equation

dt = – dv

integrating both sides, we get

t = – v + c

substituting the value of v and c in above equation