Question

Differential Equations

\text { 1. } \vec{x}^{\prime}=\left[\begin{array}{ll} 2 & 3 \\ 3 & 2 \end{array}\right] \vec{x}

(a) Draw direction field. Use the points: (0,0), (±1,0), (0,±1), (±1,±1).

(b) Draw the phase portrait.

(c) Classify the equilibrium solution with its stability.

Suppose 2x2 matrix A has eigenvalues –3 and –1 with eigenvalues 1/1 and 1/-2

O Find the general solution of 7' = A7.

(b) Draw the phase portrait.

(c) Classify the equilibrium solution with its stability.

1and3[:]3. Suppose 2 × 2 matrix A has eigenvalues {1/3] ans {1*1]

- Draw the phase portrait.

Find the general solution of 7' = A7.

(c) Classify the equilibrium solution with its stability.