1 / 8

Differential Equations

Differential Equations. Sec 6.3: Separation of Variables. Separation of Variables. all x terms can be collected with dx, and all y terms with dy, and a solution can be obtained by integration.

earl
Télécharger la présentation

Differential Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Differential Equations Sec 6.3: Separation of Variables

  2. Separation of Variables • all x terms can be collected with dx, and all y terms with dy, and a solution can be obtained by integration. • Such equations are said to be separable, and the solution procedure is called separation of variables.

  3. Examples: Separation of Variables

  4. Practice Problem • Find the general solution of the differential equation:

  5. Practice Problem: Particular Solution • Given the initial condition y(0) = 1, find the particular solution of the differential equation:

  6. Practice Problem:Particular Solution Curve • Find the equation of the curve that passes through the point (1, 3) and has a slope of y/x2 at any point (x, y).

  7. Application: Wildlife Population • The rate of change of the number of coyotes N(t) in a population is directly proportional to 650 – N(t), where t is the time in years. The population was initially at 300. After 2 years, the population increased to 500. Find the population when t = 3.

  8. Luxury is a necessity that begins when necessity ends. --- Coco Chanel Fin…

More Related