Homogeneous differential equations
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Contents |
Educational level: this is a tertiary (university) resource. |
Type classification: this is a lesson resource. |
Subject classification: this is a mathematics resource. |
Completion status: this resource is ~25% complete. |
School:Mathematics > Topic:Differential_Equations > Ordinary Differential Equations > Homogeneous Differential Equations
Homogeneous[edit]
Definition[edit]
The word “homogeneous” can mean different things depending on what kind of differential equation you’re working with. A homogeneous equation in this sense is defined as one where the following relationship is true:
Solution[edit]
The solution to a homogeneous equation is to:
- Use the substitution where is a substitution variable.
- Implicitly differentiate the above equation to get .
- Replace and with these expressions.
- Solve for .
- Substitute with the expression Then solve for .
The advantage of this method is that the function is in terms of 2 variables, but we simplify the equation by relating and to each other.