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Unformatted text preview: Section 4.4 Method of Undetermined Coefficients March 10, 2009 Method of Undetermined Coefficients Today’s Session Today’s office hours: 46 PM (Brenae is about to deliver!! and we wish her well). A useful website: http://www.quickmath.com/ A Summary of This Session: (1) Various methods of finding the particular solution (2) particular solution with the root of the characteristic equation appears in the forcing term (3) Nonsynchronous solution when w n = w (4) A lot of work by example Method of Undetermined Coefficients Polynomial Forcing Function Example 1 (a) Solve y ′′ + 3 y ′ + 2 y = 0 (b) Find a particular solution of y ′′ + 3 y ′ + 2 y = 5 (c) Find a particular solution of y ′′ + 3 y ′ + 2 y = 3 x (d) Find a particular solution of y ′′ + 3 y ′ + 2 y = 3 x + 5 (e) Find a particular solution of y ′′ + 3 y ′ + 2 y = x 2 + 3 x + 5 Answer: (a) y = C 1 e − 2 x + C 2 e − x ; (b) y p = 5 2 (c) y p = − 9 4 + 3 2 x (d) y p = 1 4 + 3 2 x (e) y p = 2 + 1 2 x 2 Method of Undetermined Coefficients Analysis of Example 1 Observation: If y 1 is a particular solution of y ′′...
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This note was uploaded on 04/07/2009 for the course MATH taught by Professor Lotfi during the Spring '09 term at Arizona.
 Spring '09
 Lotfi
 Math, Differential Equations, Equations

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