Math 210, Spring 2013
Lab Quiz #3 solutions
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Q#1
Enter the function below, then the answers are just one line Maple commands
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(a)
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(b)
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JCErd0MnXCVRISM2
(c)
QyQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkSSJmRzYiSSJ4R0YoIiIi
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(d)
LUkmbGltaXRHNiI2JEkiZkdGJC9JInhHRiRJKWluZmluaXR5RyUqcHJvdGVjdGVkRw==
IiIh
(e) I used the expression tab on the left to enter the definite integral form
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LUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJi1JJGNvc0dGJDYjKiRJInhHRiciIiMiIiIsJiokRi4iIiVGMEYwRjAhIiIvRi47IiIkIiIm
Couldn't do the integral symbolically, we'll have to use a numerical approximation
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JCErJjRoOUMiISM3
Q #2 The equilibrium points are the roots of the RHS function
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Plot the function over different intervals until I see three roots
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Find the three zeros seen above more accuractely
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Considering the sign of the derivative of f at the equilibrium points seen from the graph, x2 is stable and x1 and x3 are unstable.
Q#3
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Q#4
Specify the DE and the initial condition, then use dsolve to find the solution
QyQ+SSNkZUc2Ii8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkidUdGJTYjSSJ0R0YlRi4sJiokRisiIiMiIiIhIiJGMkYy
Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiNJInRHRilGKywmKiRGJyIiIyIiIiEiIkYv
QyQ+SSNpY0c2Ii8tSSJ1R0YlNiMiIiEjIiIiIiIjRiw=
Ly1JInVHNiI2IyIiISMiIiIiIiM=
LUknZHNvbHZlRzYiNiQ8JEkjZGVHRiRJI2ljR0YkLUkidUdGJDYjSSJ0R0Yk
Ly1JInVHNiI2I0kidEdGJSwkLUkldGFuaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCZGJyIiIi1JKGFyY3RhbmhHRis2IyNGMCIiIyEiIkY2
Isolate the expression on the LHS above as the solution.
QyQ+SSVzb2xuRzYiLUkkcmhzRyUqcHJvdGVjdGVkRzYjSSIlR0YlIiIi
LCQtSSV0YW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJkkidEdGKCIiIi1JKGFyY3RhbmhHRiU2IyNGLCIiIyEiIkYy
The range of the plot was not specified, I tested a few things until I saw that it was tending to an equilibrium point.
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