In a DiffEQ video, the problem y' = (x^2 + 3y^2) / (2xy) is solved as a homogeneous differential equation. The steps are all fine and the solution is found to be x^2 + y^2 - Cx^3 = 0.
If the answer is correct, then the derivative of the solution should equal the RHS of the question. Am I understanding DiffEQs correctly?
If yes, then what's wrong here? I take the derivative of the solution and solve for y'
2x + 2y y' -3Cx^2 = 0
y' = (3Cx^2 - 2x) / (2y).
But I don't see how to make that look like the question. My derivative looks correct, so what am I missing?