8.3.9 Systems of ordinary differential equations

Problem: Solve the system of homogeneous linear differential equations, using Euler's method: \[ \dot{x}=\left(\begin{array}{ccc} 4 & -5 & 7 \\ 1 & -4 & 9 \\ -4 & 5 & 0 \end{array}\right) \cdot X \text {. } \]