Lab 03 Expectations

Submit Plots: 1, 2, 4 (2 graphs), 5

1. Dfield7 plot of your chosen differential equation with 4-6 solutions and explanation about the theorems.
2. a) Dfield7 plot of the given differential equation with 4-6 solutions. What kind of curves do they seem to be, and where do they appear to cross?
   b) Find the general solution to the equation in #2, and show that the curves do cross where you expected. Which hypothesis isn’t satisfied?
   c) Find the exact solution using x(1)=seed.
   d) Find the exact solution to x(0)=0 and relate your answer to the theorems.
   e) Find the exact solution using x(0)=seed and relate your answer to the theorems.
3. Why do you expect the solution to exist and be unique? Using Dfield7 plot several windows and write your observations. Why can’t you answer your boss’s question?
4. Solve the IVP. Make 2 distinct Dfield7 plots with tracings as prescribed in the lab write-up. What is the formula for t<1 and t>1? Explain why this function satisfies the IVP.
5. Show that x(t)=0, 2, and 4 are solutions to the IVP. Using the second IVP, what can you conclude about x(t)? Use Dfield7 to plot the solution to the IVP. Does this support your conclusion about x(t)?