EGR 265, TEST I 1

EGR 265, Math Tools for Engineering Problem Solving

February 13, 2013, 50 minutes

TEST I

Name: ..........................................

Problem 1

Problem 2∗

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Total

EGR 265, TEST I 2

Problem 1 (4+4+4+4 Points)

Determine the order of the following ODEs. Also, state if they are linear or non-linear.

(a) y′′ −y2=x

(b) y(3) −y′=xy

(c) x

y=y′

(d) (y′ex)′= cos x

Problem 2∗(8 Points Bonus)

Find the values of the constant cfor which the function y=c

x2is a solution of the diﬀerential

equation

xy′+y=x2y2.

Warning: This DE is neither separable nor linear, thus we don’t have a method to systemat-

ically ﬁnd its solutions.