The general solution of the DEx √(1 + y^2) dx + y √(1 + x^2) dy = 0 is A^. sin-1 + sin^-1 = C

Question

The general solution of the DEx \(\sqrt{1\,+ x^2}\) dx + y \(\sqrt{1\,+ y^2}\) dy = 0 is 

A. sin^-1 x + sin^-1 y = C

B. \(\sqrt{1\,+ x^2}\) + \(\sqrt{1\,+ y^2}\) = C

C. tan^-1x + tan^-1y = C

D. None of these

Answer 1

Let 1 + y² = t and 1 + x² = u

2y dy = dt and 2x dx = du

On integrating on both sides we get