Homogeneous differential equations

A differential equation that contains two homogeneous functions of the same degree in two variables is called the homogeneous differential equation.

Introduction

In differential equations, the homogeneous functions in two variables are appeared in some cases. So, it is essential to learn the procedure of solving the differential equations in which the homogeneous functions are involved.

Let’s assume that $f(x, y)$ and $g(x, y)$ represent two homogenous functions in two variables $x$ and $y$. The corresponding differentials are $dx$ and $dy$. For solving the homogenous differential equations, the differentials are shifted to one side of the equation and homogenous functions are shifted to the other side of the equation, but it is possible if they are expressed in ratio form as follows.

$\dfrac{dy}{dx} \,=\, \dfrac{f(x, y)}{g(x, y)}$

Problems

The list of homogeneous differential equations questions with solutions to learn how solve the homogenous differential equations in calculus.