Solve the following differential equations: x√(1 - y^2)dx + y√(1 - x^2)dy = 0)

Question

Solve the following differential equations:

\(x\sqrt{1-y^2}dx + y\sqrt{1-x^2}dy=0\)

Answer 1

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

integrating both sides, we get

substituting the value of v and c in above equation