- Consider the differential equation y
^{ó}= 2 - x - y, where a is a positive constant. One (and only one) of the following slope field plots is definitely not associated with this differential equation. Which plot*does not*correspond to the differential equation? Explain why not. - Suppose that y(x) is a solution of the initial value problem
y(0.2) = 1, y
^{ó}= x^{2}+ y. Use Euler's method with Dx = 0.1 to estimate y(0.5). -
Make a rough sketch of the slope field for the differential equation [dy/ dx] = 2.5 y - 7.5. Find an equilibrium solution and determine from the plot if it is stable or unstable. Explain why.

- A yam has been heated to 170 degrees Fahrenheit and is placed in a room
whose temperature is maintained at 70 degrees F.
In half an hour the yam cools to 100 degrees F.
Let Y(t) be the temperature of the yam at time t hours
after it was placed in the room.
a) Assume the Newton's law of cooling applies, write a differential equation satisfied by Y(t).

b) Solve the differential equation to find a formula for Y(t).

- A drug is given intravenously at a rate of 5 mg/hr.
The drug is excreted frmo the patient's body at a rate proportional
to the amount present, with constant of proportionality equal to 0.2.
No drug is present at time 0.
a) Write a differential equation satisfied by Q(t).

b) If treatment is continued for a long, long time, how much of the drug will be present in the body?

- Solve the initial value problems:
a) y [dy/ dx] -

^{x}/_{y}= 0, y(1) = 2.b) [dr/ dx] + x e

^{r}= e^{r}, r(1) = 0. - The growth of certain population is
described by the differential equation
[dP/ dt] = 0.001 (800 P - P
^{2}), where P(t) is the population at time t days. The initial population is 25 mill.a) What is the population at the time when the population is growing most rapidly?

b) Will the population ever exceed 900 mill.? Explain.

- The following is data corresponding to certain population.
t (days) 0 1 2 3 4 5 6 P (mill) 3.975 7.2 12.825 23.55 37.65 57.0 79.27 [dP/ dt] ^{1}/_{P}[dP/ dt]

a) Use the data to calculate approximately the blanks in the table.b) Use (a) to plot

^{1}/_{P}[dP/ dt] versus P,c) fit a line as best you can through the points, and then obtain a differential equation satisfied by P.

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