1
AMS 361: Applied Calculus IV by Prof. Y. Deng
Quiz 3
Wednesday (04/27/2011) at 3:505:10PM in 137 Harriman
(1)
Closed book test with 1page (doublesided 8.5x11) formulas
(2)
Do any two of the three problems. If all three are attempted, the two (and only two) best 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
NO NAME NO GRADES
Problems
Score
Remarks
Q21
Q22
Q23
Total Score
Q31 (5 Points):
Find the general solution for
!
!
!
!!!
+
4
!
!
!
!!
+
!
!
!
−
!
=
1
+
!
+
!
!
∀
!
>
0
Solution:
First, we introduce a new variable
!
with the expression
!
=
!"#
. Then
!
=
!
!
.
We convert those nonlinear terms as some linear ones:
!
!
!
=
!
!
!
!
!!
=
!
−
!
!
!
!
!!!
=
2
!
−
3
!
+
!
where
!
,
!
,
!
are 1
st
, 2
nd
and 3
rd
order derivative of y with respective to t, respectively.
Then the original ODE is converted into the following form:
!
+
!
−
!
−
!
=
1
+
!
!
+
!
!
!
We come into solving a new constantcoefficient nonhomogeneous O.D.E.
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 Spring '08
 Staff
 Laplace, Characteristic polynomial, Complex number, st nd rd

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