$$
\text {If the Wronskian W of f and g is } 3e^{4t}
\text {, and if f(t)=} e^{2t}
\text {, find g(t)}
$$
$$
\begin{bmatrix}
e^{2t} & g(t) \\
2e^{2t} &g'(t)
\end{bmatrix}
$$
$$
g'(t)*e^{2t}-2e^{2t}=3e^{4t}
$$
$$
g'(t)-2g(t)=3e^{2t}
$$
$$
So, p(t)=-2
$$
$$
Therefore,\mu=e^{-2t}
$$
$$
e^{-2t}g'(t)-2e^{-2t}g(t)=3e^{2t}*e^{-2t}
$$
$$
(e^{-2t}g(t))'=3
$$
$$
e^{-2t}g(t)=3t+c
$$
$$
g(t)= \frac {3t+c}{e^{-2t}}\
$$
