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Do Now: #36 and 38 on p.322

Do Now: #36 and 38 on p.322. Evaluate. Do Now: #36 and 38 on p.322. Evaluate. Section 6.2b. Separation of Variables. Separable Differential Equations. A differential equation is separable. if can be expressed as a product of a function of.

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Do Now: #36 and 38 on p.322

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  1. Do Now: #36 and 38 on p.322 Evaluate

  2. Do Now: #36 and 38 on p.322 Evaluate

  3. Section 6.2b Separation of Variables

  4. Separable Differential Equations A differential equation is separable if can be expressed as a product of a function of and a function of . The differential equation then has the form:

  5. Separable Differential Equations If , we can separate the variables by dividing both sides of the equation by h(y), obtaining, in succession, We can now find a solution for the differential equation by integrating each side separately…

  6. Practice Problems Solve the differential equation Since is never zero, we can solve by separating the variables: On the left:

  7. Practice Problems Solve the differential equation Since is never zero, we can solve by separating the variables: On the right:

  8. Practice Problems Solve the differential equation Since is never zero, we can solve by separating the variables: Combining the constants of integration: This gives y as an implicit function of x. We can give yas an explicitfunction of x by simply solving for y…

  9. Practice Problems Solve the differential equation

  10. Practice Problems Solve the differential equation On the left:

  11. Practice Problems Solve the differential equation (Note: technically, C is now C’ = C/2, but C’s are generic)

  12. Practice Problems Solve the differential equation

  13. Practice Problems Solve the initial value problem: Initial condition:

  14. Practice Problems Solve the initial value problem: On the right:

  15. Practice Problems Solve the initial value problem: Initial condition:

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