Problem: Consider the initial value problem = 2 - x 5 - x x = 0 when t = 0 Do th

Question

Problem:   Consider the initial value problem

                           =   2 - x5 - x

                        x = 0 when t = 0

Do the following.

1.      Read section 2.5.2 (Numerical solution of differential equations) of the online notes.

2.      (2 points) Try using the DSolve function in Mathematica to solve this initial value problem. What happens? In parts 2 - 4, turn in a printed copy of your input to and output from Mathematica.

3.      (2 points) Use the NDSolve function in Mathematica to obtain a numerical approximation to the solution of this initial value problem for 0 £ t £ 10.

4.      (2 points) Use Mathematica to plot the solution for 0 £ t £ 10. If necessary, use the PlotRange option to Plot so that the plot shows the entire graph of the solution x(t) as t varies from 0 to 10.

5.      (2 points) What happens to x(t) as t ® ¥?

6.      Review your notes on the lecture about qualitative behavior of solutions of differential equations of the form dx/dt = f(x). Then answer the following questions.

a.      (1 points) What is f(x) for the differential equation

   =   2 - x5 - x

b.      (2 points) What are the equilibrium points for this differential equation?

c.      (2 points) For what values of x is f(x) positive and for what values of x is f(x) negative?

d.      (2 points) Using your answer to parts b and c explain how you could have obtained the answer to part 5 without doing parts 3 and 4.

Explanation / Answer

i cont give answer for this, simbols like ®, ¥,x5 are not understand

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.