Differential equations/Change of variables
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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. |
Definition[edit]
In a differential equation, if a certain term appears many different times, a substitution can be made similar to a -substitution.
Solution[edit]
- Substitute a term for a variable (e.g. ).
- Implicitly differentiate the variable (e.g. ).
- Solve for the derivative that needs to be solved (e.g. ).
- Solve the original equation in terms of and then use the substitution for to get the original equation back in terms of and .