[Math] Particular solution to differential equation

Question

$\frac{dy}{dx}$=$\frac{3}{2y}$ and y=4 when x=5

I started with 2y dy = dx

I don't think I started off right.

My teachers solution:

Answer 1

Note that $$\int 2y \ dy=\int 3\ dx$$ Integrate each side gives $$y^2=3x+K$$ So when $y=4$, $x=5$ gives $K=1$ So$$y^2=3x+1$$