Applied Mathematical Methods

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Second Order Linear Non-Homogeneous ODE’s

This chapter builds up on the work of the previous one and completes the task of solving linear second order ODE’s. Its primary focus is the development of methods of undetermined coefficients and variation of parameters.

Linear ODE’s and Their Solutions

Continuing on the theme introduced at the end of the previous chapter, we can erect an analogy between the problems of solving a linear system of equations Ax = b and a linear differential equation of the kind y″ + Py′ + Qy = R over an interval. Let us assume, in the first case, that the system is consistent and, in the second, that P(x), Q(x), R(x) are continuous in the interval; i.e. both of the problems do have solutions. Next, suppose we have found ...