Math 2300 Section 005 – Calculus II – Fall 2010

Notes on Separation of Variables – October 27, 2010

Definition: We call a differential equation separable if it can be written in the form

for a function of and a function of .

The Formal Approach to Solving Separable Differntial Equations

If then we can write

Integrating both sides with respect to the variable gives

What will usually happen is that this introduces a natural log in terms of . Exponentiating and solving for then provides a solution in terms of .