Module for Homogeneous Functions

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

Background

    A function f(x,y) is said to be homogeneous of degree zero provided that  f(tx,ty) = f(x,y).  In this case, the substitution   will produce the function  .  

Definition. If f(x,y) is homogeneous of degree zero, then we call the differential equation a homogeneous first order D.E.

Theorem.  Let    be a homogeneous first order D.E.  The change of variable y(x) = x v(x) will convert the D.E. to a separable differential equation.

Example 1.  Solve the differential equation  .  

Example 2.  Solve the differential equation  .  

Example 3.  Find the general solution to first order D. E.  .