Find the relation that exists between \(P(x)\) and \(Q(y)\) if the equation \[\frac{d^2y}{dx^2} + P\frac{dy}{dx} + Qy = 0\] has two non-zero solutions one of which is the square of the other. Show that the condition \[y'' - \left(3x + \frac{1}{x}\right)y' + 2x^2y = 0,\] and hence obtain the complete solution of this equation.