MATH 295/287(DE): DIFFERENTIAL
EQUATIONS
TEMPLATE NOTES FOR TRENCH
CHAPTERS 1-7 AND 9
About these notes:
These notes were written based on the videos for this My Open Math
Differential Equations online template. The content of these notes is based
on specific sections of the book and specific videos with in each section.
These notes are the same as the agendas, but space is provided for note
taking. The videos that these notes are based from are embedded in the RA-
DE MOM assignments.
• Print these notes. I recommend printing all of them, having them
three-hole punched, and keep them in a binder. As you move through
the RA-DE assignments, take notes on these template notes, giving
you reference material as you complete RA-DE homework problems.
Of course, you may choose to download these notes, so you can take
notes using a writeable device (tablet, Ipad, etc.).
• When you plan to begin learning a specific section, just start the RA-
DE assignment (found on MOM calendar). Take notes and do
homework problems as they arise.
• Alternatively, select the desired chapter from the course content folder
to find the RA-DE assignments as well as a link to the desired
textbook section.
, TABLE OF CONTENTS
READING ASSIGNMENT (RA-DE) SECTION PAGE
RA-DE 1.2 3
RA-DE 1.3 6
RA-DE 2.1 9
RA-DE 2.2 12
RA-DE 2.3 17
RA-DE 2.4 22
RA-DE 2.5 25
RA-DE 2.6 26
RA-DE 2.7 27
RA-DE 2.8 31
RA-DE 2.9 33
RA-DE 3.1 35
RA-DE 3.2 36
RA-DE 3.3 37
RA-DE 4.1 38
RA-DE 4.4 40
RA-DE 4.5 46
RA-DE 4.8 49
RA-DE 4.2 52
RA-DE 4.3 55
RA-DE 4.7 59
RA-DE 4.10 63
RA-DE 4.6 65
RA-DE 5.1 69
RA-DE 5.4 71
RA-DE 5.5 73
RA-DE 5.6 76
RA-DE 5.7 79
RA-DE 5.8 81
FA-DE 8.1 86
RA-DE 8.2 93
RA-DE 8.3 97
RA-DE 8.4 101
RA-DE 9.1 102
RA-DE 9.2 105
RA-DE 9.3 108
, RA-DE 1.2
VIDEO #1
SOLUTIONS TO DIFFERENTIAL EQUATIONS
Example:
*
# '(
Verify 𝑦 = #$ 𝑥 &is a solution to the differential equation ') = 𝑥𝑦 + on the interval
(-∞, ∞).
, Example:
Verify 𝑦 = 4cos(2𝑥 ) + 6 sin(2𝑥 ) is a solution to 𝑦 :: + 4𝑦 = 0 on the interval (-∞, ∞).
Example:
'+ ( '(
Is 𝑦 = 𝑒 =) + 2𝑥𝑒 =) a solution to ') +
+ 2 ') + 𝑦 = 0 on the interval (-∞, ∞).
EQUATIONS
TEMPLATE NOTES FOR TRENCH
CHAPTERS 1-7 AND 9
About these notes:
These notes were written based on the videos for this My Open Math
Differential Equations online template. The content of these notes is based
on specific sections of the book and specific videos with in each section.
These notes are the same as the agendas, but space is provided for note
taking. The videos that these notes are based from are embedded in the RA-
DE MOM assignments.
• Print these notes. I recommend printing all of them, having them
three-hole punched, and keep them in a binder. As you move through
the RA-DE assignments, take notes on these template notes, giving
you reference material as you complete RA-DE homework problems.
Of course, you may choose to download these notes, so you can take
notes using a writeable device (tablet, Ipad, etc.).
• When you plan to begin learning a specific section, just start the RA-
DE assignment (found on MOM calendar). Take notes and do
homework problems as they arise.
• Alternatively, select the desired chapter from the course content folder
to find the RA-DE assignments as well as a link to the desired
textbook section.
, TABLE OF CONTENTS
READING ASSIGNMENT (RA-DE) SECTION PAGE
RA-DE 1.2 3
RA-DE 1.3 6
RA-DE 2.1 9
RA-DE 2.2 12
RA-DE 2.3 17
RA-DE 2.4 22
RA-DE 2.5 25
RA-DE 2.6 26
RA-DE 2.7 27
RA-DE 2.8 31
RA-DE 2.9 33
RA-DE 3.1 35
RA-DE 3.2 36
RA-DE 3.3 37
RA-DE 4.1 38
RA-DE 4.4 40
RA-DE 4.5 46
RA-DE 4.8 49
RA-DE 4.2 52
RA-DE 4.3 55
RA-DE 4.7 59
RA-DE 4.10 63
RA-DE 4.6 65
RA-DE 5.1 69
RA-DE 5.4 71
RA-DE 5.5 73
RA-DE 5.6 76
RA-DE 5.7 79
RA-DE 5.8 81
FA-DE 8.1 86
RA-DE 8.2 93
RA-DE 8.3 97
RA-DE 8.4 101
RA-DE 9.1 102
RA-DE 9.2 105
RA-DE 9.3 108
, RA-DE 1.2
VIDEO #1
SOLUTIONS TO DIFFERENTIAL EQUATIONS
Example:
*
# '(
Verify 𝑦 = #$ 𝑥 &is a solution to the differential equation ') = 𝑥𝑦 + on the interval
(-∞, ∞).
, Example:
Verify 𝑦 = 4cos(2𝑥 ) + 6 sin(2𝑥 ) is a solution to 𝑦 :: + 4𝑦 = 0 on the interval (-∞, ∞).
Example:
'+ ( '(
Is 𝑦 = 𝑒 =) + 2𝑥𝑒 =) a solution to ') +
+ 2 ') + 𝑦 = 0 on the interval (-∞, ∞).
