Exercises

01

Complex eigenvalues

Solve the system ${\mathbf{y}}^{\prime }=\left(\begin{array}{cc}3& -13\\ 5& 1\end{array}\right)\mathbf{y}$. First find the complex solutions, then find the real solutions.

02

Insufficient eigenvectors

Solve the IVP: $\begin{array}{rl}{x}^{\prime }(t)& =7x+y\\ y^{\prime }(t)& =-4x+3y,\end{array}$ $\left(\begin{array}{c}x(0)\\ y(0)\end{array}\right)=\left(\begin{array}{c}2\\ -5\end{array}\right)$.