ABSTRACT
Ordinary differential equations may be solved, in some circumstances, using a method of separation of variables. This involves collecting terms
involving like variables and integrating. If the differential equation can be expressed in the form:
then the solution is found by integrating to give:
(first order equation)
A function f(x,y) is said to be homogeneous and of degree n if for some value of k:
yxfkkykxf n ,, For example:
Homogeneous of degree 2
C id h fi d diff i l i b l h M( ) d N( )
Homogeneous of degree 0
ons er t e rst or er erent a equat on e ow w ere x,y an x,y are both homogeneous and of the same degree:
Homogeneous of degree 0
,Now,
because homogeneous
The first equation can thus be expressed in the form:
Putting y = vx, where v is a new variable, we have an equation in which the variables are separable.
