Solving $\frac{dP}{dt} = P(a - b\sqrt P)$ using separation of variables I need to solve the following differential equation using separation of variables but I am unsure on how to do this
$$
\frac{dP}{dt} = P(a - b\sqrt P)
$$
Where $p(0) = 4$, $a = 0.302$ and $b =0.002$
I tried substituting $P = u^2$ as a change of variables to help me solve the equation.

Identifying this as a Bernoulli equation with $n=\frac32$ gives the parametrization $u=P^{1-n}\iff P=u^{-2}$ so that
$$
P'=-2u^{-3}u'=u^{-2}(a-bu^{-1})
\\
\implies -2u'=au-b
\\
\implies au(t)-b=(au(0)-b)e^{-at/2}
$$
which should allow to fully solve this problem.
