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Unformatted text preview: dy t y dt t y ) 6 3 ( ) 3 4 ( 2 2 4 3 3 3 y y y x x y x Summary of Overall Technique: To solve an exact firstorder equation: 1. Put the equation in the form ) , ( ) , ( dy y x N dx y x M 2. Start with M x f and integrate with respect to x to find f . f will involve arbitrary function of y 3. Differentiate f from step 2 with respect to y and set this equal to N . Can now solve for arbitrary function of y 4. C y x f ) , ( is the solution. MATH2860U: Chapter 2 cont… 3 Example: ) 3 ( ) 1 6 ( 2 dy y x dx xy Example: Solve x y y x y 2 ) 2 ( subject to 7 ) ( y MATH2860U: Chapter 2 cont… 4 Example: Solve dy y x dx x y 1 2 2 subject to 2 ) 1 ( y Example: ) sin ( ) 3 cos 2 ( 2 3 2 dx dy y y x x y x y x...
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This note was uploaded on 10/29/2010 for the course DEFFERENTI 2080 taught by Professor Kidnan during the Spring '10 term at UOIT.
 Spring '10
 Kidnan

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