09-22-review - Differential Equations — Fall 2011...

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Unformatted text preview: Differential Equations — Fall 2011 Friday, 9/22/11 In-class review for Sections 4.2–4.5 1 Find the general solution to the differential equation y + 4y + 13y = 0. 2 Find the general solution to the differential equation y − 4y + 4y = e2t . 3 Find the general solution to the differential equation y + y + y + y = 0. Hint: one of the roots of the corresponding characteristic polynomial is r = −1. Flip over for one more problem... Differential Equations — Fall 2011 4 Friday, 9/22/11 In an initial value problem, you are given a differential equation, together with a value of y and a value of y . In a boundary value problem, on the other hand, you are given a differential equation and two values of y (we think of these as the values of y “on the boundary”). The following questions concern the boundary value problem y + λ2 y = sin t; y (0) = 0; y (π ) = 1. a. Find the general solution to the given differential equation for all λ = ±1 (ignoring the boundary conditions for now). b. Find the general solution to the given differential equation when λ = ±1 (again ignoring the boundary conditions). c. Show that the boundary value problem has a solution if and only if λ is not an integer. ...
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This note was uploaded on 12/10/2011 for the course MAP 2302 taught by Professor Tuncer during the Fall '08 term at University of Florida.

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09-22-review - Differential Equations — Fall 2011...

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