MAT 3237 Differential Equations Section 2.2 Separable Equations

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Presentation transcript:

MAT 3237 Differential Equations Section 2.2 Separable Equations

Quiz Quiz: 2.2 WebAssign 2.2

Section 2.2 This section is covered in Calculus II if you took it here. It is considered as a review.

Differential Equations Let y be a function in x A D.E. is an equation involves x, y, y’, y’’, … Our goal is to solve for the solutions y(x)

Approach (Toolbox) Given a D.E. Identify the type/nature of the D.E. 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) 4. is called the particular solution of the D.E. Remarks

Solution Curves

Example 2

Expectations for Partial Fractions Should be done one the side (right hand column). State the partial fractions with unknown coefficients. Clearly show how you solve for the coefficients. At the end, write down the solved partial fractions.

Remarks

Example 2

Example 3

Review: We learned… how to solve separable equations. how to fix the integration constant if initial condition is given. how to deal with absolute values in the process of solving DE. The presentation requirements for partial fractions. solution curves and singular solutions.

Classwork Work with a partner and ONLY one partner. Liz and I will check your work (normally) until 5:50 (may be 6:00). Finishing your classwork in time will positively affect your class participation grade.