06-01-2023

Problem: Consider the system of linear differential equations \begin{align*} \frac{\mathrm{d} x_1}{\mathrm{d} t} & = 5x_1 - 2x_2 \\ \frac{\mathrm{d} x_2}{\mathrm{d} t} & = 4x_1 - x_2 \end{align*} with the initial conditions $x_1(0)=0$ and $x_2(0)=-1$. The find out the value of $\log_e\left( x_2(2)-x_1(2) \right) $.

Solution: