Transcription of Nonhomogeneous Linear Equations - Stewart …
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Nonhomogeneous Linear Equations - Stewart …
Nonhomogeneous Linear EquationsIn this section we learn how to solve second-order Nonhomogeneous Linear differential equa-tions with constant coefficients, that is, Equations of the formwhere , , and are constants and is a continuous function. The related homogeneousequationis called the complementary equationand plays an important role in the solution of theoriginal Nonhomogeneous equation (1).TheoremThe general solution of the Nonhomogeneous differential equation (1)can be written aswhere is a particular solution of Equation 1 and is the general solution of thecomplementary Equation we have to do is verify that if is any solution of Equation 1, then is asolution of the complementary Equation 2.
NONHOMOGENEOUS LINEAR EQUATIONS 3 EXAMPLE 3 Solve . SOLUTION We try a particular solution Then so substitution in the differential equation gives or This is true if The solution of this system is
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