Module for the Cauchy-Euler Differential Equation

Numerical Methods for O. D. E. using Mathematica. (c) John H. Mathews, 2003

Background

    A Cauchy-Euler differential equation has the form  

        .  

Use the change of variable  z = ln x  to construct a new D. E. with  Y  being a function of  z,  

        .  

The solution to this latter D. E. has the form  

        .

Then the solution to the Cauchy-Euler D. E. is

        .  

Exercise 1.  Solve the Cauchy-Euler differential equation  .  

Exercise 2.  Solve the Cauchy-Euler differential equation  .  

Exercise 3.  Solve the Cauchy-Euler differential equation  .