1
AMS 361: Applied Calculus IV by Prof. Y. Deng
Quiz 3
Wednesday (04/25/2012) at 5:20PM-6:40PM in 001 ESS
(1)
Closed Book with 1-page (double-sided 8.5x11) self-prepared 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 for a total of 10 points (max).
(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.
(5)
No name, no grade and no question asked or answered.
SB ID
Name
Problems
To
Grade?
Score
Remarks
Q2-1
Q2-2
Q2-3
Total Score
Q3-1
(5 Points): Find the general solution of the following non-homogeneous DE
using your favoriate method:
࠵
!
࠵
!!
+
2
࠵
!
࠵
!
−
12
࠵
!
࠵
=
1
Solution
: Method I (Undetermined Coefficients)
This problem is a Cauchy-Euler equation, so its solution should be a polynomial. To
find the homogeneous solution, use the trial function
࠵
=
࠵
!
and plug into the
homogeneous equation first
࠵
!
࠵
!
!!
+
2
࠵
!
࠵
!
!
−
12
࠵
!
࠵
!
=
࠵
࠵
−
1
+
2
࠵
−
12
࠵
!
!
!
=
࠵
!
+
࠵
−
12
࠵
!
!
!
=
0
⇒
࠵
+
4
࠵
−
3
=
0
⇒
࠵
=
−
4
࠵±
࠵
=
3
Thus,
࠵
!