Chapter 2.4, Problem 2E

In Exercises 1-4, we consider the system
$\begin{array}{l}\frac{dx}{dt}=2x+2y\\ \frac{dy}{dt}=x+3y\end{array}$

For the given functions $Y(t)=\left(x\left(t\right),y\left(t\right)\right)$ , determine if $Y(t)$ is a solution system.

2. $\left(x\left(t\right),y\left(t\right)\right)=\left(3e^{2t}+e^t,-e^t+e^{4t}\right)$