Euler and Legendre Equations

An Euler equation has the general form

Euler equations can be solved by transforming them to equations with constant coefficients.

This is an example of an Euler equation.
In[1]:=
Click for copyable input
Out[1]=

The Legendre linear equation is a generalization of the Euler equation. It is an ODE of the form

Here is an example of a Legendre linear equation.
In[2]:=
Click for copyable input
Out[2]=