To solve the separable differential equation $$\frac{x^2}{y^2-3}\frac{dy}{dx} = \frac{1}{2y} ,$$ we must find two separate integrals:
$\int$ $dy =$
and
$\int$ $dx =$
The first integral we integrate by substitution:
$u =$ $du =$
Solving for y we get one positive solution $y =$ and one negative solution $y =$ (Note: you must simplify all arbitrary constants down to one constant k)
Find the particular solution satisfying the initial condition $$y(1) = -5.$$
$y(x) =$ .