Homogeneous Functions
One is that a first-order ordinary differential equation is homogeneous (of degree 0) if it has the form
where x is an independent variable, y a dependent variable, and M(x, y) and N(x, y) are homogeneous functions of degree n; in other words scalar multiplying each variable by a constant λ leaves the function unchanged:
- .
In a more general form:
- .
Read more about this topic: Homogeneous Differential Equation
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