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Unformatted text preview: Section 4.5 Superposition Principle; Method of Undetermined Coefficients March 23, 2009 Superposition Principle Today’s Session Lecture 14 with the corrected equation has been updated online Clicker points (out of 23 points) have been updated on D2L. If you received a zero, most probably you either (1) never bothered to use the clicker; (2) You do not have a clicker; (3) Your clicker is one of the one that has no associated username. In case of (3), come by my office, bring your clicker along and I will rectify this matter. A useful website: http://www.quickmath.com/ A Summary of This Session: (1) Superposition Principle (2) More examples Superposition Principle Reminder Decide whether or not the method of undetermined coefficients can be applied to solve the given dfq. In case it does, find the particular solution: y ′′ + 2 y ′ y = t − 1 e t Answer: We can’t at this stage, since the leading power is negative integer. y ′′ + 2 y ′ y = te t Answer: y p = ( 1 + t / 2) e t . Superposition Principle Superposition Principle (p. 196) Suppose y 1 is a solution to the dfq a y ′′ + b y ′ + c y = f 1 ( t ) and suppose y 2 is a solution to the dfq a y ′′ + b y ′ + c y = f 2 ( t ) Then α y 1 + β y 2 is a solution to a y ′′ + b y ′ + c y = α f 1 ( t ) + β f 2 ( t ) Superposition Principle Example 1 (a) Find particular solutions to y ′′ + 3 y ′ + 2 y = e 10 t and y ′′ + 3 y ′ + 2 y = te − 2 t (b) Find a particular solution to y ′′ + 3 y...
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 Spring '09
 Lotfi
 Differential Equations, Equations, Boundary value problem, Qn

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