1
AMS 361: Applied Calculus IV by Prof. Y. Deng
Quiz 2
Wednesday (03/30/2011) at 3:50PM5:10PM in 137 Harriman
(1)
Closed Book with 1page (doublesided 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
Q21
Q22
Q23
Total Score
Q21 (5 points):
For a given variable coefficient homogeneous DE,
!
!
!
!
!
!
+
!
!
!"
!"
+
!
!
!
=
!
one solution is given as
!
!
!
≠
!
. Find the general solution of this DE by finding
another linearly indepdent solution
!
!
!
=
!
!
!
!
!
.
Please note that
!
!
!
,
!
!
and
!
!
are given functions while
!
!
is not.
Solution:
First we must take all necessary derivatives of
!
!
!
,
!
!
!
(
!
)
=
!
!
!
!
+
!
′
!
!
!
!
!!
(
!
)
=
!
!
!
!!
+
!
!
!
!
!
′
+
!
′′
!
!
Plugging these values into the original DE, we obtain:
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 Spring '08
 Staff
 Derivative, linearly independent solution, Prof. Y. Deng, linearly indepdent solution

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