1. Math 231: Differential Equations Set 2: Solving Variables Separable Type Differential Equations Notes abridged from the Power Point Notes of Dr. Richard Rubin

2. 1st Order Differential Equations We will start our consideration of how to solve ordinary differential equations by considering the simplest possible type: We know something about finding y from the Fundamental Theorem of Calculus. What do we know?

3. 1st Order Differential Equations We will start our consideration of how to solve ordinary differential equations by considering the simplest possible type: Do you remember: Method of Substitution? Example:

4. Separable Equations Many differential equations that you will come across can not be solved using the methods of integral calculus. We will now set out to develop some general methods of attack for DE. The first of the types we will consider is called Separable Equations.

5. Separable Equations Definition: A first order differential equation of the form: is said to be separable if

6. Separable Equations Can you see how?! This step accomplishes the separation. Now what? How do we solve?

7. Separable Equations Example:

8. Separable Equations Example:

9. Separable Equations Example:

10. 1st Order Differential Equations Homework: Be sure to do ‘pencil and paper’ solutions before you do the Maple solutions! You get the most out of this way!