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

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Problem 1 (8 points)

Find an explicit solution of the initial value problem

exydy

dx = 1, y(0) = 2.

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?

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.