Exercises
Differential equations
Problems to solve on your own. The final solution appears with the button below each problem; each exercise also has its own page, to share with the link.
1. General solution by separation of variables
Find the general solution of
Solution available to those who have unlocked the subject.
2. Separable equation with the cosine
Find the general solution of
Solution available to those who have unlocked the subject.
3. Cauchy problem with a bounded interval of existence
Solve the Cauchy problem and state the interval of existence of the solution:
Solution available to those who have unlocked the subject.
4. Cauchy problem with an interval of existence on a half-line
Solve the Cauchy problem and state the interval of existence of the solution:
Solution available to those who have unlocked the subject.
5. First-order linear equation with constant coefficients
Find the general solution of
Solution available to those who have unlocked the subject.
6. Linear equation with a coefficient depending on x
Find the general solution, for , of
Solution available to those who have unlocked the subject.
7. Cauchy problem for a first-order linear equation
Solve the Cauchy problem
Solution available to those who have unlocked the subject.
8. Bernoulli equation with an exponential term
Find the general solution of
Solution available to those who have unlocked the subject.
9. Bernoulli equation with constant coefficients
Find the general solution of
Solution available to those who have unlocked the subject.
10. Polynomial particular solution by the method of undetermined coefficients
Find the general solution of
Solution available to those who have unlocked the subject.
11. Homogeneous equation with distinct real roots
Find the general solution of
Solution available to those who have unlocked the subject.
12. Homogeneous equation with complex roots
Find the general solution of
Solution available to those who have unlocked the subject.
13. Method of undetermined coefficients with resonance
Find the general solution of
Solution available to those who have unlocked the subject.
14. Second-order Cauchy problem with a double root
Solve the Cauchy problem
Solution available to those who have unlocked the subject.