EGR 265, Spring 2012, Final Exam 1

EGR 265, Math Tools for Engineering Problem Solving

May 7, 2012, 10:45am to 1:15pm

Name (Print last name ﬁrst): ..........................................

Student ID Number: ......... ...... ............

Final Exam

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Total

EGR 265, Spring 2012, Final Exam 2

Problem 1 (8 points)

Find an explicit solution of the initial value problem

y′−2x= 2xy, y(1) = 0.

EGR 265, Spring 2012, Final Exam 3

Problem 2 (10 points)

A liquid is heated to 100◦F. It cools down according to Newton’s law of cooling in a

surrounding medium of temperature 50◦F. The rate of cooling is k=−0.5.

(a) State the diﬀerential equation which governs the temperature of the medium at

time taccording to Newton’s law of cooling.

(b) Solve this diﬀerential equation with the correct initial value (this can be done either

as a separable or a linear equation).

(c) At what time has the temperature dropped to 75◦F? (Logarithms do not need to

be evaluated.)