Question

The general solution of the differential equation x(1 + y²)dx + y(1 + x²)dy = 0 is (1 + x²)(1 + y²) = k.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Because given equation can be written as `(2x)/(1 + x^2) "d"x = (-2y)/(1 + y^2) "d"y`

⇒ log(1 + x²) = – log(1 + y²⁾ + log k

⇒ (1 + x²)(1 + y²) = k