Math 1220
Quiz 11
Due: December 1
Answer the questions below. The value of each question is indicated at the
beginning of it. Please indicate which convergence test you are applying in
each case.
Name:
UID:
1. Use a power series expansion to show that the differential equation
y 00 (x) + y(x) = 0,
has solution y(x) = cos x.
y(0) = 1,
y 0 (0) = 0
2. In quiz 6 you showed that the differential equation
y 00 (x) + 4y 0 (x) + 5y(x) = 10ex ,
y(0) = 1,
y 0 (0) = 2
has solution
y(x) = ex + e−2x sin x
(i) Find a power series expansion in x of the function
f (x) = ex + e−2x sin x
through terms of order 3.
(ii) Find the power series expansion of the solution to the differential equation
y 00 (x) + 4y 0 (x) + 5y(x) = 10ex ,
y(0) = 1,
y 0 (0) = 2
through terms of order 3. You should recover the series in part (i).
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