4Second-Order Linear Equations

DOI: 10.1201/9781003214526-4

  • Second-order linear equations

  • The nature of solutions of second-order linear equations

  • General solutions

  • Undetermined coefficients

  • Variation of parameters

  • Use of a known solution to find another

4.1 Second-Order Linear Equations with Constant Coefficients

Second-order linear equations are important because (considering Newton's second law) they arise frequently in engineering and physics. For instance, acceleration is given by the second derivative, and force is mass times acceleration.

In this section we learn about second-order linear equations with constant coefficients. The “linear” attribute means, just as it did in the first-order situation, that the unknown function and its ...

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