(v)quad x^(2)=2y^(2)log y;(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

y^(2)dx+(x^(2)+xy+y^(2))dy=0

x^(2)dy+(x^(2)-xy+y^(2))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

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