Question

Solve the linear system dx/dt = -y and dy/dt=4x to determine whether the critical point (0,0) is stable, asymptotically stable, or unstable. Use a computer system or graphing calculator to construct a phase portrait and direction field for the given system. Thereby ascertain the stability of instability of each critical points, and identify it visually as a node, a saddle point, a center, or a spiral point.