Differential Equations and Infinite Series for Engineering Students

Mathematics 69.105, Section D, Winter, 2000.

Homework Page

NOTE: This page will be updated weekly.

Week 1:

Section 9.2 # 3, 9, 11
Section 9.2 # 15, 17, 19, 21

Week 2:

Section 9.4 # 3, 5, 7, 9, 11
and Tutorials 1 and 2

Week 3:

Section 9.3 # 6, 7, 8, 9
and Tutorial 3

Week 4:

Section 9.4 #1, 3, 5, 7, 9, 11
and Tutorial 4

Section 9.6 #1, 3, 5

Week 5:

Section 9.7 #1, 3, 5, 7, 9, 11, 15, 25, 27, 29

Week 6:

Section 9.8 #1, 3, 5, 7, 9

More 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

Week 8:

Sequences and series

Section 8.1, p. 450 # 1 - 25 (odd)
Section 8.2 p. 457 # 1 - 9 (odd)
Section 8.3, p. 469 # 1 - 25 (odd)

Week 9:

Sequences and series

Section 8.1, p. 477 # 1 - 11 (odd)

Week 10:

Sequences and series

Section 8.5, p. 488 # 1 - 7 (odd)
Section 8.6, p. 497 # 1 - 13 (odd)

Week 11:

Sequences and series

Section 8.7, p.502 # 13,15,17

Section 8.8, p. 505 # 1,3

Section 8.9, p. 509 # 1,3,9

Week 12:

Sequences and series

Section 9.9, p. 567 # 5

Section 9.9, p. 567 # 9, 11, 15

Week 13:

Review