Homogeneous Differential Equation
A differential equation is homogeneous if all terms involve the dependent variable or its derivatives, so is a solution.
Definition 4.8 (Homogeneous Differential Equation)
A differential equation is homogeneous if all terms involve the dependent variable or its derivatives. This implies that is a solution (trivial solution).
Example
Example 4.12
Consider the equation
We should try . Then
Which leads to (given that )
So .
This is the general solution, as it contains an arbitrary constant .
Related
Stated in
- Definition 4.8 (Homogeneous Differential Equation)§4.2 First Order Linear Ordinary Differential Equations
- Example 4.12§4.2.1 Homogeneous Linear ODEs with Constant Coefficients