Exercise 2

Verify whether or not the given pair of functions, $(x(t), y(t))$ form a solution to the system $$\begin{aligned} \frac{dx}{dt} & = 4x -3y \\ \frac{dy}{dt} & = 3x + 4y \end{aligned}$$

1. $x(t) = 2e^{4t}\cos 3t$, $y(t) = 2e^{4t}\sin 3t$

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

3. $x(t) = 3e^{4t}\cos 3t - 4e^{4t}\sin 3t$, $y(t) = 3e^{4t}\sin 3t + 5e^{4t}\cos 3t$

4. $x(t) =c_1e^{4t}\cos 3t - c_2e^{4t}\sin 3t$, $y(t) = c_1e^{4t}\sin 3t + c_2e^{4t}\cos 3t$