x^2 + y^2 = r^2 ; x(dy/dx) + r√(1 + (dy/dx)^2) = y

Question

Verify that the given function is a solution of the differential equation.

x² + y² = r² ; x\(\frac{dy}{dx}\) + r\(\sqrt{1+\left(\frac{dy}{dx}\right)^2} = y\)

x² + y² = r² ; x(dy/dx) + r√(1 + (dy/dx)²) = y

Answer 1

x² + y² = r² ……. (1)

Differentiating both sides w.r.t. x, we get

Hence, x² + y² = r² is a solution of the D.E.