Abel's Theorem

Purpose:

To use a CAS to find a second solution of a differential equation given a solution.

Description:

Abel's Theorem is used to derive a formula to find a second solution y₂(x) of y'' + p(x) y' + q (x) = 0 which is linearly independent of the given solution y₁(x). Students are asked to use this formula to write a simple program in Maple or Mathcad which finds y₂(x) given y₁(x). They then use their program to find the general solutions for some second order linear differential equations.

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