Verify that x^2 = 2y^2log y is a solution of the differential equation (x^2 + y^2) -dy/xy = 0.

Question

Verify that x² = 2y²log y is a solution of the differential equation \((x^2+y^2)\cfrac{dy}{dx}-xy=0.\)

(x² + y²) -dy/xy = 0.

Answer 1

Given \(x^2=2y^2logy\)

On differentiating both sides with respect to x, we get

Multiply both sides with y