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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.
- Fall '08