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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.

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Differential Equations

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  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…

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