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Calculus II (MAT 146) Dr. Day Monday, March 19, 2018

Calculus II (MAT 146) Dr. Day Monday, March 19, 2018. Differential Equations (Chapter 9) What is a Differential Equation? (9.1) What is a Solution to a Differential Equation? (9.1) Graphical Representations of Solutions to Differential Equations (9.2). What is a Differential Equation ?.

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Calculus II (MAT 146) Dr. Day Monday, March 19, 2018

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  1. Calculus II (MAT 146)Dr. Day Monday, March 19, 2018 • Differential Equations (Chapter 9) • What is a Differential Equation? (9.1) • What is a Solution to a Differential Equation? (9.1) • Graphical Representations of Solutions to Differential Equations (9.2) MAT 146

  2. What is a Differential Equation? • A differential equation is an equation that contains one or more derivatives. • Here’s a differential equation you have already solved: • y’ = 2x • What is the solution of this differential equation? MAT 146

  3. What is a Solution to a Differential Equation? • A general solutionto a differential equation is a family of functions that satisfies a given differential equation. • A particular solutionto a differential equation (also called the solution to an initial-value problem) is a particular function that satisfies both a given differential equation and some specified ordered pair for the function. MAT 146

  4. DE Warm-Ups • For the differential equation here, what are the constant solutions? • Solve this initial-value problem: MAT 146

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  12. Solve the differential equation graphically by generating a slope field and then sketching in a solution: y’ = 2x – y knowing that (0,0) satisfies y MAT 146

  13. y’ = 2x – y with initial conditions (0,0) MAT 146

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  21. Solving Differential Equations Solve for y: y’ = −y2 MAT 146

  22. Separable Differential Equations MAT 146

  23. Separable Differential Equations Solve for y: y’ = 3xy MAT 146

  24. Separable Differential Equations Solve for z: dz/dx+ 5ex+z = 0 MAT 146

  25. Separable Differential Equations MAT 146

  26. Separable Differential Equations MAT 146

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