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Homogeneous Differential Equations

A Differential Equation is an equation with a function and one or more of its derivatives:

Example:

an equation with the function y and its derivative

Homogeneous Differential Equations

A first order Differential Equation is Homogeneous when it can be in this form:

We can solve it using Separation of Variables but first we create a new variable

With we can solve the Differential Equation.

Example

First, get it in  form

Now, we have a function of (y/x).

Then, substitute

We’ll get

Now use Separation of Variables:

Put C in ln form with C = ln k

Now substitute back

We got the solution.

Learn More

Implicit Differentiation

Differentiable

Common Derivatives

Integration by Substitution (Reverse Chain Rule)

Calculus Index

Categories: Calculus
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