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1) Solve the following IVP:

y

00 + 6y

0 + 5y = δ(t − 2), y(0) = 0, y0

(0) = 0

2) Find the Laplace Transform of the periodic triangular wave, given by:

f(t) = 2t, 0 ≤ t < 2 and f(t + 2) = f(t)
3) Solve the integral equation:
y(t) = t +
Z t
0
y(x)dx +
Z t
0
(t − x)y(x)dx
4) Use the convolution theorem to find
L −1
s
2
(s
2 + 1)2
5) Use a power series about the point x = 0 to solve the following differential equation:
y
00 − xy0 − y = 0
Obtain a recursion formula for the coefficients and write the first 3
nonzero terms of the power series of each of the two linearly independent
solutions. Include the interval of convergence of the power series.

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