Question

Find the general solution of the ODE:

x²(y′)² + yy′(2x+y) + y²= 0

Answer 1

Since the solution technique is not mentioned analytic/numerical. I am giving a numerical solution using MATHEMATICA. If you are not convinced with the solution you can ignore the solution and no need to consider this problem for payment.

DSolve[x^2*(y'[x])^2 + y[x]*y'[x]*(2*x + y[x]) + (y[x])^2 == 0, y[x], x]

This produces the solution

That is first solution is

and the second solution is