# 4-11s-Final exam

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31 Jan 2019
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EGR 265, Spring 2011, Final Exam 1
EGR 265, Math Tools for Engineering Problem Solving
May 2, 2011, 10:45am to 1:15pm
Name (Print last name ﬁrst): ..........................................
Student ID Number: ......... ...... ............
Final Exam
P1 : P2 :
P3 : P4 :
P5 : P6 :
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P9 : P10 :
P11 :
Problem 1 (8 points)
Find an explicit solution of the initial value problem
exydy
dx = 1, y(0) = 2.
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EGR 265, Spring 2011, Final Exam 2
Problem 2 (8 points)
Note: In this problem write your answers in terms of natural logarithms, which do not
need to be evaluated.
Iodine-131 has a half-life of 8 days.
(a) Find its decay rate k.
(b) If the initial amount of Iodine-131 is 1 gram, how much of it is left after 2 days?
(c) How long does it take for Iodine-131 to decay to 10 percent of its original amount?
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EGR 265, Spring 2011, Final Exam 3
Problem 3 (14 points)
Consider the second order diﬀerential equation
y′′ 10y+ 25y= 30x+ 3.(1)
(a) Find the general solution of the homogeneous equation corresponding to (1).
(b) Find a particular solution of the inhomogeneous equation (1).
(c) Solve the initial value problem given by (1) and initial conditions y(0) = 1, y(0) = 3.
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