Solution of Some Second-Order Differential Equations with Constant Coefficients

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if , ,


You can vary the controls to get special forms of that occur most frequently in practice: zero, trigonometric, polynomial, and exponential functions.


Contributed by: Roberta Grech (September 2014)
Open content licensed under CC BY-NC-SA



Snapshot 1: the case , , , corresponds to simple harmonic motion

Snapshot 2: the case where is a quadratic function and

Snapshot 3: a failure case: , hence the complementary function is of the form , and since , the particular integral is of the form , where is a constant


[1] L. Bostock, S. Chandler, and C. Rourke, Further Pure Mathematics, Cheltenham, UK: Stanley Thornes, 1990 pp. 274–285.

[2] J. Berry, T. Graham, R. Porkess, and P. Mitchell, MEI Structured Mathematics: Differential Equations, 3rd ed., Abingdon, UK: Hodder Murray, 2006 pp. 74–141.

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