AMATH 250 Online Assignment 3
微分方程Assignment代写 Late penalty is 1% per hour. It is your responsibility to make sure you have time to upload your assignment by the deadline.
Late penalty is 1% per hour. It is your responsibility to make sure you have time to upload your assignment by the deadline.You may use the course materials posted on the course website and the optional text as references. You are also allowed to discuss ideas with your classmates, the course instructor and TAs. Please do not post fifinal answers or give away too much on Piazza; it will be monitored closely. Your submitted work must be written upon your own and should indicate your knowledge of the material.
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- The work I submit here is entirely my own
- I have not used any unauthorized aids
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Each question should be uploaded separately to Crowdmark. 微分方程Assignment代写
- Find the family of solutions to the following DEs.
- Consider the initial value problem.
(a) Find any equilibrium solutions of the di↵erential equation.
(b) Find an explicit expression for the general solution of the di↵erential equation. 微分方程Assignment代写
(c) Find an explicit expression for the solution of the initial value problem. Determine the interval of validity of the solution.
(d) Use the di↵erential equation to determine where the slope of the family of curves corresponding to the general solution is zero, positive and negative.
(e) Find the vertical and horizontal asymptotes of the family of curves corresponding to the general solution.
(f) Sketch the members of the family of curves corresponding to two values of the arbitrary constant in your general solution. Include and identify in your sketch the curve corresponding to the solution of part (c). Also include and identify any equilibrium solutions you found in part (a).
- Consider the following population model
(a) Show that the di↵erential equation can be written in the form
where k, A, B are positive constants.
(b) Solve the initial value problem.
(c) Determine the time that the population extincts (N(T) = 0). Round your answer to one decimal place.
