1
AMS 361: Applied Calculus IV by Prof. Y. Deng
Quiz 1
Wednesday (03/09/2011) at 3:50PM-5:10PM in 137 Harriman
(1)
Closed Book with 1-page (double-sided 8.5x11) formulas.
(2)
Do any two of the three problems. If all three are attempted, the two best (and only
two) will be graded.
(3)
Each problem is worth 5 points.
(4)
No points for guessing work and for solutions without appropriate intermediate steps;
Partial Credits are Given only for Steps that are Relevant to the solutions.
SB ID:
Class ID:
Name:
Problems
To
Grade?
Score
Remarks
Q1-1
Q1-2
Q1-3
Total Score
Q1-1 (5 points):
It is obvious that
𝒚
=
𝒂
satisfies the following DE. With this info, find
its general solution
𝒅𝒚
𝒅𝒙
= [
𝒇
(
𝒙
) +
𝒚
+
𝒂
](
𝒚 − 𝒂
)
where
𝒇
(
𝒙
)
is a given well-behaved function and “
a
” is a given constant.
Solution:
Substition:
𝑦
=
𝑎
+
1
𝑧
We get
𝑑𝑦
𝑑𝑥
=
−
1
𝑧
2
𝑑𝑧
𝑑𝑥
Substitute to the original DE, we get
𝑑𝑧
𝑑𝑥
+ (
𝑓
(
𝑥
) + 2
𝑎
)
𝑧
+ 1 = 0
Which is a 1
st
order linear DE and solvable with the integrating factor method:

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