# Solve the following differential equations: 2x^(2)y (d^(2)y)/(dx^(2))+4y^(2)=x^(2)(dy/dx)^(2)+2xy(dy/dx)?

Aug 11, 2018

 y = x^2(C_1+C_2 ln x)^2

#### Explanation:

Making the change of variables $y \left(x\right) = {x}^{2} {z}^{2}$ and substituting into the DE we get

 4x^5 z^3(z'+x z'') = 0

so assuming $z \setminus \ne 0$ we have

 z'+xz'' = 0\to z = C_1+C_2 ln x

and then

 y = x^2(C_1+C_2 ln x)^2