# Solution of Some Second-Order Differential Equations with Constant Coefficients

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if , ,

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Contributed by: Roberta Grech (September 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

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

References

[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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