Differential Equations Practice Exams

Time: 1 hour

Problem 1. Solve the IVP

Use the nullclines technique to sketch the solution on the phase plane.

Answer.

Problem 2. Consider the system

Show that every non-equilibrium solution lies on a straight-line. Discuss the fate of solution curves on these lines....

Answer.

Problem 3. Consider the system

(a)

Check that

is a solution.

(b)

Use Euler's method with step-size 1 and 0.5 to approximate this solution, and check how closely the approximate solutions is to the real solution when t=4, and t=6.

Answer.

Problem 4. Consider the system

(a)

Find the equilibrium points.

(b)

Find the nullclines and draw the vector field on the phase plane.

(c)

Draw some solutions (at least four).

(d)

Discuss the fate of the solutions near the equilibrium points.

Answer.

[CyberExam] [Calculus] [Differential equations]

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