4. A fish pond has a carrying capacity of 1000 fish, and an intrinsic growth rate of 0.1, expressed in number of fish per year. Let y(t) denotes the number of fish in the pond after t years. If 24 fish are harvested per year, write the differential equation for y. Plot solutions for y from initial values of 100, 500, and 800. Use the graph of z = y' in your analysis. What is the least amount fish needed initially in order to sustain a population? [Hint: To find the constant solutions (zeroes of y'), multiply the equation 0= y' by 1000 and factor.] X 5. Use Euler's method with
4. A fish pond has a carrying capacity of 1000 fish, and an intrinsic growth rate of 0.1, expressed in number of fish per year. Let y(t) denotes the number of fish in the pond after t years. If 24 fish are harvested per year, write the differential equation for y. Plot solutions for y from initial values of 100, 500, and 800. Use the graph of z = y' in your analysis. What is the least amount fish needed initially in order to sustain a population? [Hint: To find the constant solutions (zeroes of y'), multiply the equation 0= y' by 1000 and factor.] X 5. Use Euler's method with
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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#4 only
![ant solutions.
2. Draw the graph g(y) = cos(y) for 0 ≤ y ≤ 27, and then use it to help you sketch solutions of
cos(y) satisfying y(0) = 3/4, y(0) = 5/4, and y(0) = 7n/4. Also include the constant
y =
solutions.
3. A savings account earns a 4% annual rate, compounded continuously, and $500 per year is withdrawn
continuously. Let y(t) denote the value of the account after t years. Write the differential equation
for y. Use the graphical method to plot two different solutions for y, one with initial amount above
the constant solution, one below. What is the behavior of these two solutions?
4. A fish pond has a carrying capacity of 1000 fish, and an intrinsic growth rate of 0.1, expressed in
number of fish per year. Let y(t) denotes the number of fish in the pond after t years. If 24 fish are
harvested per year, write the differential equation for y. Plot solutions for y from initial values of 100,
500, and 800. Use the graph of z = y' in your analysis. What is the least amount fish needed initially
in order to sustain a population? [Hint: To find the constant solutions (zeroes of y'), multiply the
equation 0 = y' by 1000 and factor.]
I
5. Use Euler's method with n = 4 to find the approximate value of y(2) if y' = 4t - 4y and y(0) = 1.
Then find the exact value of y(2) be solving the DE. (You will need to use integration by parts.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ba8b794-0d60-45e8-bedb-9cd956db072f%2F0a7821f8-c293-41d6-bd45-a26a764e9e0a%2Fbiyce8k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ant solutions.
2. Draw the graph g(y) = cos(y) for 0 ≤ y ≤ 27, and then use it to help you sketch solutions of
cos(y) satisfying y(0) = 3/4, y(0) = 5/4, and y(0) = 7n/4. Also include the constant
y =
solutions.
3. A savings account earns a 4% annual rate, compounded continuously, and $500 per year is withdrawn
continuously. Let y(t) denote the value of the account after t years. Write the differential equation
for y. Use the graphical method to plot two different solutions for y, one with initial amount above
the constant solution, one below. What is the behavior of these two solutions?
4. A fish pond has a carrying capacity of 1000 fish, and an intrinsic growth rate of 0.1, expressed in
number of fish per year. Let y(t) denotes the number of fish in the pond after t years. If 24 fish are
harvested per year, write the differential equation for y. Plot solutions for y from initial values of 100,
500, and 800. Use the graph of z = y' in your analysis. What is the least amount fish needed initially
in order to sustain a population? [Hint: To find the constant solutions (zeroes of y'), multiply the
equation 0 = y' by 1000 and factor.]
I
5. Use Euler's method with n = 4 to find the approximate value of y(2) if y' = 4t - 4y and y(0) = 1.
Then find the exact value of y(2) be solving the DE. (You will need to use integration by parts.)
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