MAT 1235 Calculus II Section 9.3 Separable Equations I

HW and … WebAssign 9.3 Part I (15 problems, 123min.) Wednesday: 9.5 Thursday: 9.3 Part II

Differential Equations

Many “phenomenon” can be modeled /described by D.E.

Example 0.1 (Chemistry) Reaction

Example 0.2

Example 0.3 Pendulum

Example 0.4 q = charge on the capacitor

Toolbox Approach Given a differential equation Identify the type/nature of the differential equation. Use the specified techniques to solve for the solutions.

Separable Equations Technique: Separation of Variables

Example 1

1. is called the general solutions of the D.E. 2. We can verify the solution by differentiation. Remarks

3. The value of C can be fixed if additional condition is given. e.g. y(0)=4 (initial condition) Remarks

3. The value of C can be fixed if additional condition is given. e.g. y(0)=4 (initial condition) 4. is called the particular solution of the D.E. Remarks

Solution Curves

Example 2

Remarks

Example 2

Example 3