MAT 3237 Differential Equations Section 2 4 Exact

MAT 3237 Differential Equations Section 2. 4 Exact Equations http: //myhome. spu. edu/lauw

HW l

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Recall l Differentiation Implicit Differentiation Partial Differentiation

Recall l

Recall l

Recall l Solution D. E.

Recall l

Preview l l l Solving exact D. E. , which always* give implicit solutions. The solution process involves the antiderivatives of partial derivatives. View the process as the reverse operation of implicit differentiation

Exact D. E. l

Exact D. E. l The general solutions* is

Criterion Use the definition to check the exactness of a D. E. is difficult. Instead, we use Theorem 2. 1 is exact if and only if

Criterion

Example 1 (a) (b) (c) Verify that the D. E. is exact Solve the exact D. E. Use implicit differentiation to verify the solutions

Example 1(a)

Example 1(b) l

Antiderivatives: Derivatives Vs Partial Derivatives

Antiderivatives: Derivatives Vs Partial Derivatives

Antiderivatives: Derivatives Vs Partial Derivatives No new notations…

Example 1(b)

Example 1(c)

Pay Attention to the Presentation l l The connection statements are curial for your audience to understand your solutions. You do not need to use the exact wordings, but you need put down the arguments carefully.

Expectations l l The connection statements are curial for your audience to understand your solutions. You do not need to use the exact wordings, but you need put down the arguments carefully.

Common misconceptions l