Differential Equations and Infinite Series for Engineering Students

Mathematics 69.105, Section D, Winter, 1998.

Homework Page

Week 1:

Section 15.1 # 1-10 (odd)
Section 15.2 # 1, 3, 5, 7, 9
Section 15.2 # 15, 17, 19, 25

Week 2:

Section 15.2 # 25
Section 12.3 # 3 - 16 (odd)
Section 12.3 # 17 - 33 (odd)

Week 3:

Section 15.3 # 1 - 13 (odd)
Section 15.3 # 15-16
Section 15.3 # 23, 25, 27

Week 4:

Section 15.4 # 5 - 19 (odd)
Section 15.5 # 1-17 (odd)
Section 15.5 # 21, 23
Section 15.5 # 29, 31, 33

Week 5:

Section 15.6 # 1 - 10 (odd)
Look at the additional examples here.. ("Examples using Variation of Parameters").

Week 6:

Homework on Cauchy-Euler Equations

1. Find the general solution of the equation

x2y" - 3xy' + 4y = x + x2ln(x)

Answer: y = c1x2 + c2x2ln(x) + x + x2ln3(x)/6.

2. Find the general solution of the equation

x2y" - 2xy' + 2y = ln2(x) - ln(x2)

Answer: y = c1x + c2x2 + (1/4) + {ln(x) + ln2(x)}/2.

3. Find the general solution of the equation

x2y" - xy' + 4y = cos (ln(x)) + x sin (ln(x))

Answer: y = c1x cos(sqrt(3) ln(x)) + c2x sin(sqrt(3) ln(x)) + {x sin(ln(x))}/2 + { 3 cos(ln(x)) - 2 sin (ln(x)) }/13


Homework on Clairaut's Equation

1. Find the general solution of the equation

3 (y')3 + x y' = y

Answer:... y = y(x) = Cx + 3 C3

2. Solve the differential equation

x ey'(x) + x2y'(x) = x y(x)
Answer:... y = y(x) = Cx + eC


Homework on Elementary Systems of Equations

1. Find the general solution of the 2 by 2 system of equations

x' + 2x + y' + y = t

5x + y' + 3y = t2 .........Please note the misprint here!

Answer: ... y = y(t) = c1 cos(t) + c2 sin(t) + 2 t2 - 3t - 4
x = x(t) = {c1 -3 c2} sin(t) / 5 - {3 c1 + c2} cos(t) / 5 - t2 + t + 3.


Week 7 was Reading Week .................

Week 8:

Sequences and series

Section 10.1 # 1 - 39 (odd)
Section 10.2 # 1 - 31 (odd)
Section 10.3 # 1 - 21 (odd)

Week 9:

Sequences and series

Section 10.3 # 25, 27
Remainders ...

Week 10:

Sequences and series

Section 10.4 # 1 - 31 (odd)
Section 10.5 # 1 - 19, 25, 27, 29 (odd)
Section 10.6 # 1 - 31 (odd)
NEW: Section 10.7 # 1 - 19 (odd)

Week 11:

Sequences and series

NEW: Section 10.8 # 3- 19 (odd)
Section 10.10 # 1, 3, 7, 9, 11 (odd)
Section 10.10 # 17-25 (odd)
Section 10.10 # 27, 29

Week 12:

Sequences and series

Section 10.11 # 1-9, (odd)
Section 15.8 # 1-11, (odd)

Week 13:

Review Chapter 15