## Differential Equations Practice Exams

**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.

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[CyberExam]
[Calculus]
[Differential equations]
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