Differential equations/Homogeneous differential equations

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Homogeneous[edit | edit source]

Definition[edit | edit source]

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 | edit source]

The solution to a homogeneous equation is to:

  1. Use the substitution where is a substitution variable.
  2. Implicitly differentiate the above equation to get .
  3. Replace and with these expressions.
  4. Solve for .
  5. 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.