Differential equations/Change of variables
In a differential equation, if a certain term appears many different times, a substitution can be made similar to a -substitution.
- 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 .