Harold Washington College
Math 210
Final Test
Name:
Date:
00
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(1) Use series to find the solution of the differential equation (x2 −1)y +3xy +xy = 0
0
with y(0) = 4, y (0) = 6.
(2) Show that L {(1 + e2t )2 } =
4(s2 − 4s + 2)
.
s(s − 2)(s − 4)
(3) For the differential equation
0
00
4xy +
y
+y =0
2
do the following:
(a) Show that x = 0 is a regular singular point.
(b) Find the indicial equation and the indicial roots of it.
(c) Use the Frobenius method to find two series solutions of the equation:
0
(4) Solve the first order differential equation y − 3y = 0 with y(0) = 1 using the
following methods:
(a) Separation of variables;
(b) Linear equations method;
(c) Power series method; and
(d) Laplace Transform Method.
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(5) Use the Laplace Transform Method to solve the linear equation y − y − 2y = 4t2
0
with initial conditions y(0) = 1 y (0) = 4