Unformatted text preview: AMS 361: Applied Calculus IV by Prof Y. Deng
Quiz 3 Monday (04/20/2009) at 8:059:25AM
for the following DE: Q31 (7.5 Points): Find a particular solution where α is a constant and is a given function. You may express the particular in terms of the given in some integral form (5.5 Points).
solution
Find the again (2.0 Points) for a specific
. Solution. We consider two cases:
(1)
0. We have
. . 1, we have For . . 0. The characteristic equation of the corresponding homogeneous equation is
0, α ,
α
Resulting in solutions
,
Let
(2) Let us force the condition
0
Then Therefore We notice
0
0
So we have
1 1 1 1 Therefore (Grading policy: Please don’t deduct any points for solutions without the above red lines.)
So we have 1 1
1 2 1 0 2 2 . 2 Let
1 2 1 2 We found
, , , . Therefore
We have
2
1
2
For , we get
1
2 2 1
.
2 Q32 (7.5 Points): The three linearly independent solutions for a 3rd order linear
homogenous equation
,
,
. The Wronskian of the system is defined as are given as 2 1 , 2 , 1 3 3 2 3 1 1 2 2 3 . . Without actually solving the...
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 Spring '08
 Staff
 Derivative, Elementary algebra, Characteristic polynomial, Homogeneity

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