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Warm-up

Warm-up. Start with: ln y = ln (x – 2) x+1 Simplify Take derivative: 4) Solve for dy/ dx. Determine y’, if y = (x – 2) x+1. (Use logarithmic differentiation by taking the natural log of both sides of the equation.). Differential Equations. Text – Section 5.6. Introduction.

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Warm-up

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  1. Warm-up • Start with: ln y= ln (x – 2)x+1 • Simplify • Take derivative: • 4) Solve for dy/dx. Determine y’, if y = (x – 2)x+1 (Use logarithmic differentiation by taking the natural log of both sides of the equation.)

  2. Differential Equations Text – Section 5.6

  3. Introduction • Until now the only differential equations we solved were in the form: y’ = f(x) or y” = f(x). • Now we will solve more general types of differential equations. • Example: Solve y’ = 2x dy = 2x y y dx

  4. Growth and Decay Models dydt If = ky, then y= Cekt , where C is the initial value of y, and k is the proportionality constant. For k>0, we have exponential growth, and for k<0, we have exponential decay.

  5. Examples

  6. Your Turn!

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