Differential Equations Workbook For Dummies®

2.4. Practicing Your Separation Skills

Here's your chance to practice some general separable first order differential equations. (I promise it'll be more fun than stabbing yourself in the eye, so put that pencil back down.) I include differential equations of all sorts so you can get some practice with the various possibilities. But first, a quick example.

NOTE

EXAMPLE

Q. Solve this differential equation:

A.

1. Separate the equation to get

   

2. Multiply both sides by dx:

   y dy = x² dx

3. Then integrate both sides of the equation:

   

4. Multiply by 2 (and absorb 2 into the constant c):

   

5. You're left with

   

15. Solve this differential equation by separating it:

16. What's the solution if you separate this ...