Find the solution of the differential equation x√(1 + y^2)dx + y√(1 + x^2)dy = 0.

Question

Find the solution of the differential equation \(x\sqrt{1 + y^2}dx + y\sqrt{1 + x^2} dy = 0.\)

Answer 1

We can write above differential equation as

By the method of variable separable we can write,

Integrating both sides,

Putting values in integral we get,

Putting values of t and u,

Where C is the arbitrary constant.

is the required solution of the differential equation.