Which of the following differential equations is separable?

Find the general solution to the separable differential equation $3t\frac{dw}{dt}=6t^2$.

A rumor spreads in a school according to $\frac{dS}{dt}=aS(1-\frac{S}{B})$, where $a$ is the spread rate, $B$ is the total number of students, and $S_0$ is the initial number of students who know the rumor. Find $S\left(t\right)$ in terms of $a$, $B$, $S_0$.

Find the explicit general solution to $(s^2+3{)}^{2}u{u}^{\prime }(s)=s(u^2+16)$.

Solve the initial value problem $y^{\prime }\left(x\right)=\frac{4x}{y^2-4},y\left(0\right)=2$. Leave your answer in implicit form.