Differential equations/Change of variables

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Definition[edit | edit source]

In a differential equation, if a certain term appears many different times, a substitution can be made similar to a -substitution.

Solution[edit | edit source]

  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 .