Previous page : To find particular solutions

Next page : Homogenous differential equations – a first type

We will, on the next page, look at particular type of differential equations connected to the so called homogenous function of two variables that are functions that follows this rule:

I.e., when you multiply the variables by a scale factor then the result is the same as if you instead would have multiplied the function by that scale factor to the power of some constant. That constant, *k*, is the degree of homogeneity of the function.

The function

is homogenous of degree 2 since

In general, polynomials of the form

are homogenous, as is quite easily verified, and in particular

and

A rational function of two homogenous polynomial is also homogenous. This is also easy to verify, but I leave that to you. More generally, the quotient of two homogenous function is also homogenous.

Finally we have that function of the forms

or

that are homogenous of degree 0, since any scale factor will cancel.

Up a level : Differential EquationsPrevious page : To find particular solutions

Next page : Homogenous differential equations – a first typeLast modified: