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Math 2214 Review Problems for Exam 3, Spring 2006
Show all work. No credit will be given for unsupported answers. Circle your
answers. No calculators allowed.
1. Find the general solution of y(4) + 2y"' + 2y" + 2y'+'1 = O. (Hint: (.>-2 + 1) is a factor
of the characteristic polynomiaL)
2. Rewrite (t
2
+l)ylll + (sin t)y" - (et)y = t
2
as a. system of first order equations
y'(t) = P(t)y(t) + g(t). Identify the matrix function P(t) and the vectol: functions g(t) and
y(t) .
--------
3. Compute the vVronskian of the solutions
Yl (t) = ( ~ )
e-
5t
of the system of differential equations y' = P(t)y. Could {ydt), Y2(t), Y3(t)} be a funda
mental set of solutions for such a system of differential equations where P(t) is a three by
three matrix with entries that are continuous on (-00, oo)?
4. Find the general solu tion of
(
1 0 0)
y' = 2 2 0 y.
113
5. Find the general solution of y' = Ay if A is a (2 X 2) const...

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