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SECOND ORDER (inhomogeneous)

Differential EquationsSECOND ORDER ( inhomogeneous )Graham S McDonaldA Tutorial Module for learning to solve 2ndorder ( inhomogeneous ) differential equationslTable of contentslBegin Tutorialc of on using solutionsFull worked solutionsSection 1: Theory31 TheoryThis Tutorial deals with the solution of SECOND ORDER linear swith constant coefficients (a,bandc), of the form:ad2ydx2+bdydx+cy=f(x) ( )The first stepis to find the general solution of the homogeneous equa-tion [ as ( ), except thatf(x) = 0].

This Tutorial deals with the solution of second order linear o.d.e.’s with constant coefficients (a, b and c), i.e. of the form: a d2y dx2 +b dy dx +cy = f(x) (∗) The first step is to find the general solution of the homogeneous equa-tion [i.e. as (∗), except that f(x) = 0]. This gives us the “comple-mentary function” y …

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