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Differential Equations                                        Quiz #6                                                      April 8, 2005

Name____________________                   R.  Hammack                                                 Score ______
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(1)    Find the general solution of the differential equation 4y''-12y'+9y=0.
The auxiliary equation is 4m^2-12m+9=(2m - 3)^2=0.
Therefore, there is only one (repeated) root, y = 3/2.

Solution to D.E. is y = c_1e^(3x/2)+c_2x e^(3x/2)


(2)   Find a differential operator that annihilates the function. y=cos(x/2).

D^2+1/4

(3)   Find three linearly independent functions that are annihilated by the differential operator D^3-10D^2+25D

D^3- 10D^2 + 25D = D(D - 5)^2

The functions are:
y = 1  y = e^5  y = x e^5