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Chapter 1: First-Order Differential Equations

Chapter 1: First-Order Differential Equations. Sec 1.4: Separable Equations and Applications. Definition 2.1. A 1 st order De of the form. is said to be separable. 1. 2. 3. 3. Sec 1.2. How to Solve ?. Sec 1.4: Separable Equations and Applications. 1. 2. 3. 4.

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Chapter 1: First-Order Differential Equations

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  1. Chapter 1: First-Order Differential Equations

  2. Sec 1.4: Separable Equations and Applications Definition 2.1 A 1st order De of the form is said to be separable. 1 2 3 3

  3. Sec 1.2 How to Solve ?

  4. Sec 1.4: Separable Equations and Applications 1 2 3 4 Solve the differential equation It may or may not possible to express y in terms of x (Implicit Solution)

  5. Sec 1.4: Separable Equations and Applications Solve the IVP

  6. Implicit Solutions and Singular Solutions Solve the IVP Implicit So , Particular, sol 2 -2 2 -2

  7. Sec 1.2 How to Solve ? Remember division 3) Remember division

  8. Implicit Solutions and Singular Solutions Singular Sol division Solve the IVP a general Sol Family of sol (c1,c2,..) a general Sol Family of sol (c1,c2,..) Particular Sol No C The general Sol It is a general sol Contains every particular sol Singular Sol no value of C gives this sol

  9. Sec 1.4: Separable Equations and Applications 1 2 3 4 Solve the differential equation It may or may not possible to express y in terms of x (Implicit Solution)

  10. Modeling and Separable DE Cooling and Heating Natural Growth and Decay According to Newton’s Law of cooling The Differential Equation K a constant • serves as a mathematical model for a remarkably wide range of natural phenomena. • Population Growth • Compound Interest • Radioactive Decay • Drug Elimination Torricelli’s Law Water tank with hole

  11. The population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. What will be the population in 40 years? The Differential Equation K a constant

  12. The Differential Equation K a constant

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