" (iv) "x^(2)=2y^(2)log y,quad :(x^(2)+y^(2))(dy)/(dx)-xy=0

if x^(2)=2y^(2)log y then prove (x^(2)+y^(2))(dy)/(dx)-xy=0

Verify that the given fuction (implicit or explicit) is a solution of the corresponding differential equation. x^2 = 2y^2 log y : (x^2 + y^2) (dy)/(dx) - xy = 0

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

If y=log[x+sqrt(x^(2)+a^(2))], show that ((x^(2)+a^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

If y=log{x+sqrt(x^(2)+a^(2))}, prove that: (x^(2)+a^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0