# Separable Equations & Modeling

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## Lecture Notes

#### Ordinary Differential Equations

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Section 1, Page 1 to page 2

Definition, including examples of order 0, 1, 2, and k. Homogeneous and inhomogeneous differential equations are defined.

Instructor: Prof. Jason Starr
Prior Knowledge: Derivatives (section 2 of lecture 1)

#### Separable Differential Equations

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Section 2, Page 2 to page 4

Step-by-step solutions to separable differential equations and initial value problems.

Instructor: Prof. Jason Starr
Prior Knowledge: Differentials and Antidifferentiation (lecture 13), Ordinary Differential Equations (section 1 of this lecture)

#### Applications of Differential Equations

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Section 3, Page 4 to page 6

Exponential growth as a differential equation. Worked examples of population growth, radioactive decay, and Newton's Law of Cooling.

Instructor: Prof. Jason Starr
Prior Knowledge: Differential Equations (sections 1 and 2 of this lecture)

## Online Textbook Chapter

#### Introduction to Differential Equations

Document

Definition, including the order of a differential equation as well as linear, homogeneous, inhomogeneous, and separable differential equations.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: None

## Practice Problems

#### Separable Differential Equations

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Problem 1 (page 1 to page 2)

Three part question which involves setting up and solving separable differential equations.

Instructor: Prof. Jason Starr
Prior Knowledge: None

## Exam Questions

#### Separable Ordinary Differential Equation

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Problem 3 (page 5)

Solving a separable ordinary differential equation with a given initial condition.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### Differential Equations

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Problem 10 (page 1) to problem 11 (page 1)

Two questions, one of which involves solving a first order differential equation and the other of which involves setting up and solving a differential equation for the temperature of a fish being cooked.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Differential Equations

PDF
Problem 5b (page 1)

Finding the solution to a first order differential equation.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Differential Equation

PDF
Problem 5b (page 2)

Finding the solution to a first order differential equation.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Differential Equations

PDF
Problem 7 (page 1)

Using separation of variables to find the solutions to a differential equation and describing the graphs of these solutions.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Differential Equations: Separation of Variables

PDF - 2.2 MB
Problem 3F-1 (page 25) to problem 3F-8 (page 26)

Eight questions which involve solving separable differential equations, including questions about Newton's Law of Cooling and about air pressure at different altitudes.

Instructor: Prof. David Jerison
Prior Knowledge: None