Math 242 Homework Assignments

MATH 242
Honors Elementary Differential Equations

Homework Assignments and Supplementary Materials

To view an Acrobat PDF version of each Solution Set, click on the symbol .
(Free Acrobat reader can be found here.)

Homework Assignments
(Each Problem is worth 10 pts.)

No. Assignment Due Page and No.'s

#1 Tuesday, Jan.22 p. 10: 1,2,5,11,19,21,25

#2 Thursday, Jan.24 page 32: 9
page 103-104: 7,9,10

#3 Tuesday, Jan.29 p. 57: 1,3,11,23,25
p. 69: 3,5,9

#4 Tuesday, Feb.5 Use the Maple worksheets at Maple Worksheets to assist you with the following problems from Section 2.1:
(i) p. 48-49: 5, 12, 17, 19, 21
(ii) For problem #12 of part (i) above, what is the type of differential equation (separable, linear, ...)? Derive its analytic solution.
(iii) p. 49: 26 [Extra Credit]

If you are getting "division by zero" when using initial conditions with certain slope fields in maple, try either a) printing the plot and sketching the approximate solutions by hand on the plot, or b) decrease the stepsize (delta x) in the underlying integration so that it is more accurate and does not try to cross an asymptote. An example for #12 would be
DEplot( ode, [y(x)], x=-4..4, y=-4..4,[[1.5,0]], stepsize=.01,arrows=LINE );

#5 Thursday, Feb. 7 p. 78-79: 7,13,17,23,29.
p. 91: 1,3

#6 Thursday, Feb. 14 p. 141-153: 3, 13, 31, 35(a)

#7 Thursday, Feb. 28 Modeling
p. 229: #1
Extra Credit p. 359: #14 (set-up, do not solve)
Determinants/Cramer's rule
click here.
Higher Order IVP
p. 151: #1,#3
Homogeneous Solutions
p. 152: #15,#19
General Solutions
p. 153: #23,#25,#31

#8 Tuesday, March 5 You may want to check the new Maple worksheet (here) which is related to, but not required for this assignment. We will go over this sheet briefly during class.

p. 153: #35 (Conor pointed out the typo on #31. It is not assigned and has since been deleted.)

p. 163: #3, #5, #23, #27, #31, #35

Find an ordinary differential equation of order four, so that y_1(x)=exp(x), y_2(x)=cos(2x), and y_3(x)=x exp(x) are all solutions of the equation. (Hint: Think backwards)

#9 Thursday, March 7 The annihilator method and undetermined coefficients.

p. 186: #21, #25
p. 187: #43, #47

#10 Thursday, March 21 Variation of Parameters Method

p. 192: #1, #5, #13, #19

#11 Tuesday, March 26 Cauchy-Euler Equations

p. 199: #5, #19

#12 Thursday, March 28 The Laplace Transform

p. 312: #1, #7, #15, #23, #25

#13 Thursday, April 11 The inverse Laplace Transform

p. 323: #7, #15, #23, #27

#14 Tuesday, April 16 Additional properties of the Laplace Transform and solving systems of ODE.

p. 323: #2, #5, #35; p. 358: #5
Note: The first set of problems were intended to come from page 347, not page 323. Sorry for the typo. You do not need to turn these in, but be prepared for these types of problems for the exam.

#15 Tuesday, April 23 Convolution and Laplace transform properties.

p. 347: #9, #13, #19 (b), #37

This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated May 8, 2002.
This page ©2000-2002, The Board of Trustees of the University of South Carolina.
URL: http://www.math.sc.edu/~sharpley/math242_s02

Return to Math 242 Home Page

No.	Assignment Due	Page and No.'s
#1	Tuesday, Jan.22	p. 10: 1,2,5,11,19,21,25
#2	Thursday, Jan.24	page 32: 9 page 103-104: 7,9,10
#3	Tuesday, Jan.29	p. 57: 1,3,11,23,25 p. 69: 3,5,9
#4	Tuesday, Feb.5	Use the Maple worksheets at Maple Worksheets to assist you with the following problems from Section 2.1: (i) p. 48-49: 5, 12, 17, 19, 21 (ii) For problem #12 of part (i) above, what is the type of differential equation (separable, linear, ...)? Derive its analytic solution. (iii) p. 49: 26 [Extra Credit] If you are getting "division by zero" when using initial conditions with certain slope fields in maple, try either a) printing the plot and sketching the approximate solutions by hand on the plot, or b) decrease the stepsize (delta x) in the underlying integration so that it is more accurate and does not try to cross an asymptote. An example for #12 would be DEplot( ode, [y(x)], x=-4..4, y=-4..4,[[1.5,0]], stepsize=.01,arrows=LINE );
#5	Thursday, Feb. 7	p. 78-79: 7,13,17,23,29. p. 91: 1,3
#6	Thursday, Feb. 14	p. 141-153: 3, 13, 31, 35(a)
#7	Thursday, Feb. 28	Modeling p. 229: #1 Extra Credit p. 359: #14 (set-up, do not solve) Determinants/Cramer's rule click here. Higher Order IVP p. 151: #1,#3 Homogeneous Solutions p. 152: #15,#19 General Solutions p. 153: #23,#25,#31
#8	Tuesday, March 5	You may want to check the new Maple worksheet (here) which is related to, but not required for this assignment. We will go over this sheet briefly during class. p. 153: #35 (Conor pointed out the typo on #31. It is not assigned and has since been deleted.) p. 163: #3, #5, #23, #27, #31, #35 Find an ordinary differential equation of order four, so that y_1(x)=exp(x), y_2(x)=cos(2x), and y_3(x)=x exp(x) are all solutions of the equation. (Hint: Think backwards)
#9	Thursday, March 7	The annihilator method and undetermined coefficients. p. 186: #21, #25 p. 187: #43, #47
#10	Thursday, March 21	Variation of Parameters Method p. 192: #1, #5, #13, #19
#11	Tuesday, March 26	Cauchy-Euler Equations p. 199: #5, #19
#12	Thursday, March 28	The Laplace Transform p. 312: #1, #7, #15, #23, #25
#13	Thursday, April 11	The inverse Laplace Transform p. 323: #7, #15, #23, #27
#14	Tuesday, April 16	Additional properties of the Laplace Transform and solving systems of ODE. p. 323: #2, #5, #35; p. 358: #5 Note: The first set of problems were intended to come from page 347, not page 323. Sorry for the typo. You do not need to turn these in, but be prepared for these types of problems for the exam.
#15	Tuesday, April 23	Convolution and Laplace transform properties. p. 347: #9, #13, #19 (b), #37


This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated May 8, 2002. This page ©2000-2002, The Board of Trustees of the University of South Carolina. URL: http://www.math.sc.edu/~sharpley/math242_s02