Bumper Booklet: Second Order Differential Equations

Procedurally generated questions on Second Order Differential Equations.
The skills build in complexity, and ends with a large section of mixed questions.

Designed for use by individuals or as a resource from which questions can be taken. All questions have answers.

All of these questions are fluency based skills which can be practiced repeatedly until they are second nature. That’s what this is for!

Please: Do not attempt every question in one go.

Contents (~100 per section):

1. Homogeneous 2nd Order DE’s with characteristic polynomials with two real solutions.
2. Homogeneous 2nd Order DE’s with characteristic polynomials with a repeated solution.
3. Homogeneous 2nd Order DE’s with characteristic polynomials with complex roots.
4. Homogeneous 2nd Order DE’s with characteristic polynomials (MIX)
5. Particular Solutions to Homogeneous 2nd Order DE’s given the initial conditions.
6. Simple Non-Homogeneous 2nd Order DE’s with polynomial RHS.
7. Simple Non-Homogeneous 2nd Order DE’s with exponential RHS.
8. Simple Non-Homogeneous 2nd Order DE’s with trigonometric RHS.
9. Non-Homogeneous 2nd Order DE’s with simple RHS.
10. Complicated Non-Homogeneous 2nd Order DE’s with exponential RHS.
11. Complicated Non-Homogeneous 2nd Order DE’s with trigonometric RHS.
12. Non-Homogeneous 2nd Order DE’s with exponential RHS (MIX).
13. Non-Homogeneous 2nd Order DE’s with combination RHSs (MIX).
14. Solving Non-Homogeneous 2nd Order DE’s (Complete mix).