Getting rid of a fractional power over f(x)

Question

I start with the following relation.

$\frac{dy}{\sqrt{y}} = -h dt$

I then integrate it and get this function.

$y^{\frac{3}{2}} = -\frac{3}{2}ht + C$

My algebra is rusty, so I'm stuck at this point. My desire is to get a functional relation in the form.

$y(t) = t$

How do I go about this?

Answer 1

we have $\int y^{-1/2}dy=-\int h dt$ this gives us $2y^{1/2}=-ht+C$