Solution
= Solution
On an interval excluding $t=0$, an <integrating factor> for this <first-order linear differential equation> is $t^4$. Multiplying through gives
$$
\frac{d}{dt}(t^4y)=3t^4.
$$
An <antiderivative> then gives $t^4y=3t^5/5+C$, so
$$
\boxed{y(t)=\frac35t+\frac{C}{t^4}},\qquad t\ne0.
$$
The constant is arbitrary on each connected interval of the domain; the original <differential equation> is undefined at zero.