Differential equations MOC

Homogenous first-order differential equation

A first-order ODE in the form

is homogenous of order if the functions and are both homogenous of order 𝑛;

Such an ODE may be converted to a Separable differential equation using either the substitution

The former is advantageous if is easier to integrate.

Motivation

Because of the characteristic property of homogenous functions, the ratio of the functions can be expressed as a function of a single variable . Let . Then,

Practice problems

• https://www.mathsisfun.com/calculus/differential-equations-homogeneous.html

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