1. Warmup 3/30/16 In Biblical terms, a saint is any follower of Christ who has the holy spirit. Catholics have a second definition – Christians who are in heaven, or special people who have performed miracles and served Christ more than most. There are over 2,500 of them at present. What do you think of this idea / practice? To learn how to solve separable differential equations pp 455: 5, 6, 7, 8 Objective Tonight’s Homework

2. Homework Help Let’s spend the first 10 minutes of class going over any problems with which you need help.

3. Notes on Separable Differential Equations If you recall, implicit differentiation is when you can take the derivative of each part of an equation. A differential equation is the same thing but in reverse. It’s where we want to integrate with respect to each variable. In this course, we’ll deal only with what we call “separable differential equations”. These are differential equations where we can split our x and y variables to different sides of the equation. To do non-separable differential equations, you would need at least 2 more years of calculus.

4. Notes on Separable Differential Equations Example: Find the general solution to the differential equation 8y 2 x 2 dy/dx = y 3

5. Notes on Separable Differential Equations Example: Find the general solution to the differential equation 8y 2 x 2 dy/dx = y 3 This equation is separable. Separate the variables, then integrate each side. 8y 2 x 2 dy/dx = y 3 original equation 8y 2 /y 3 dy = 1/x 2 dxseparation 8/y dy = 1/x 2 dxsimplify 8 ln(y) + C = -1/x + Cintegration ln(y) = -1/8 x + Crearrange y = e -1/8 x + C solve for y

6. Group Practice Look at the example problems on pages 451 to 454. Make sure the examples make sense. Work through them with a friend. Then look at the homework tonight and see if there are any problems you think will be hard. Now is the time to ask a friend or the teacher for help! pp 455: 5, 6, 7, 8

7. Exit Question What does it mean if our function is separable? a) That there is only one solution to integrating b) That x and y can be split apart c) That it has no real-world application d) That is has dy/dx e) That it has dx/dy f) None of the above