Back to Differential Equations

Lesson PreviewLesson 5 of 7 in this unit

7.5 Finding General Solutions Using Separation of Variables

Part of Differential Equations in AP® Calculus AB. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

Start free
Some differential equations can be solved by separation of variables, which means rewriting the equation so all y terms are on one side and all x terms are on the other. Once separated, antidifferentiation can be used to find a general solution, which usually includes a constant C. This works for equations that can be put into a form like
dydx=g(x)h(y)\frac{dy}{dx}=g(x)h(y)
,
allowing us to rewrite them as
1h(y)dy=g(x)dx\frac{1}{h(y)}dy=g(x)dx
.

In this unit

7 lessons

  1. 7.1Modeling Situations with Differential EquationsPreview lesson
  2. 7.2Verifying Solutions for Differential EquationsPreview lesson
  3. 7.3Sketching Slope FieldsPreview lesson
  4. 7.4Reasoning Using Slope FieldsPreview lesson
  5. 7.5Finding General Solutions Using Separation of VariablesThis lesson
  6. 7.6Finding Particular Solutions Using Initial Conditions and Separation of VariablesPreview lesson
  7. 7.7Exponential Models with Differential EquationsPreview lesson

Continue the full lesson in Stellar

Create a free account to unlock the remaining sections, checkpoints, course practice, and progress tracking for AP® Calculus AB.

Start free