Change of variables

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School:Mathematics > Differential Equations > Ordinary differential equations > Change of variables

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]

  1. Substitute a term for a variable (e.g. ).
  2. Implicitly differentiate the variable (e.g. ).
  3. Solve for the derivative that needs to be solved (e.g. ).
  4. Solve the original equation in terms of and then use the substitution for to get the original equation back in terms of and .