Separable Equations & Modeling

Ordinary Differential Equations

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

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 1 on pages 1–2

Separable Differential Equations

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

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

• Read lecture notes, section 2 on pages 2–4

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

• Complete practice problem 1 on pages 1–2
• Check solution to practice problems 1 on pages 3–4

Applications of Differential Equations

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

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 3 on pages 4–6

Introduction to Differential Equations

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

• 18.013A Calculus with Applications, Spring 2005
  Prof. Daniel J. Kleitman

Course Material Related to This Topic:

• Read chapter 26 of online textbook

Separable Ordinary Differential Equation

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

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Complete exam problem 3 on page 5
• Check solution to exam problem 3 on page 3

Differential Equations

• 18.01 Single Variable Calculus, Fall 2006
  Prof. David Jerison

Course Material Related to This Topic:

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.

• Complete exam problems 10–1 on page 1
• Check solution to exam problems 10–1 on page 2

Finding the solution to a first order differential equation.

• Complete exam problem 5b on page 1
• Check solution to exam problem 5b on page 1
• Complete exam problem 5b on page 2
• Check solution to exam problem 5b on page 2

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

• Complete exam problem 7 on page 1
• Check solution to exam problem 7 on page 1

Differential Equations: Separation of Variables

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

• 18.01 Single Variable Calculus, Fall 2006
  Prof. David Jerison

Course Material Related to This Topic:

• Complete exam problems 3F–1 to 3F–8 on pages 25–6
• Check solution to exam problems 3F–1 to 3F–8 on pages 44–7

First Order ODE

Applet for plotting the solution to a specified differential equation of one variable with a specified initial condition, along with the approximations given by the left hand, trapezoid, and Runge–Kutta rules.

• 18.013A Calculus with Applications, Spring 2005
  Prof. Daniel J. Kleitman

Course Material Related to This Topic:

• Interact with a Java Simulation