A. Let $g(t)$ be the solution of the initial value problem
$$3 t \frac{dy}{dt} + y = 0, \ \ t > 0,$$ with $g(1) = 1 .$
Find $g(t)$.
$g(t) =$ .

B. Let $f(t)$ be the solution of the initial value problem
$$3 t \frac{dy}{dt} + y = t^{4}$$ with $f(0) = 0 .$
Find $f(t)$.
$f(t) =$ .
C. Find a constant $c$ so that $$k(t) = f(t) + c g(t)$$
solves the differential equation in part B and $k(1) = 5.$
$c =$ .