Random 2D Linear System Problems

Here are a few randomly generated problems on 2D systems of ordinary differential equations.

Quick classifications

One more classification

Given the system below, classify the origin as

• A saddle point,
• An unstable node,
• An unstable spiral,
• A stable spiral, or
• An unstable node.

Explain your answer using the full power of theorem 4.40.

Sketch a saddle

The system below should have two real eigenvalues with unequal signs. Find those eigenvalues with their corresponding eigenvectors and use that information to sketch the phase plane by hand. Your sketch should include the eigenvectors and four solutions. Snap a picture and upload.