Particular Solution of a Nonhomogeneous Linear Second-Order Differential Equation with Constant Coefficients

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This Demonstration shows the method of undetermined coefficients for a nonhomogeneous differential equation of the form with
,
,
, and
constants. If
, then the form of the particular solution is
. If
and
, the particular solution is of the form
. If
and
, the particular solution is of the form
.
Contributed by: Izidor Hafner (January 2014)
Open content licensed under CC BY-NC-SA
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Details
The general solution of a nonhomogeneous linear differential equation is , where
is the general solution of the corresponding homogeneous equation and
is a particular solution of the first equation.
Reference
[1] V. P. Minorsky, Problems in Higher Mathematics, Moscow: Mir Publishers, 1975 pp. 262-263.
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