lecture06

# lecture06 - Section 2.4 Contd Feb 3 2009 Exact Equations...

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Section 2.4, Cont’d Feb 3, 2009 Exact Equations

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Announcements WebAssign Assignment 2 is now online. The quiz this week will cover the integrating factor method Exact Equations
Today’s session: Exact equations Solve dx = 0 Answer: x = C . The solution curves are a stream of parallel vertical lines (this means solution curves never cross). Solve dF = 0 Answer: F = C . The solution curves are a stream of parallel lines (in the appropriate frame; remember: solution curves never cross). dF = 0 is called an exact equation Fact: dF = F x dx + F y dy dF is also called a total differential Exact Equations

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Exact Equation Suppose we want to solve: dy dx = - M ( x , y ) N ( x , y ) Cross multiply: M ( x , y ) dx + N ( x , y ) dy = 0 Step 1. Try to compare it with something like: F x dx + F y dy = 0 Step 2. Identify the terms. This means: F x = M ( x , y ) and F y = N ( x , y ) Exact Equations
Exact Equation, cont’d Step 3. Partial integrate one of the equation, then differentiate and match: F ( x , y ) = integraldisplay M ( x , y ) dx + C ( y ) N ( x , y ) = y

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