1) use dsolve command in matlab to find an explicit solution to dy/dx = (y-1)^2, y(0)=1

2) using matlab, plot your solution from part 1) over -5x5

3) use dsolve command to in matlab to find an explicit solution to dy/dx = (y-1)^2, y(0) = 1.01

4) using matlab, plot your solution from part 3) over -100x250

5) use dsolve command to in matlab to find an explicit solution to dy/dx = (y-1)^2 + 0.01, y(0) = 1

6) using matlab, plot your solution from part 5) over -20x20 and -5y5

7) compare the solutionsof the three IVPs using the plots created in matlab in parts 2), 4) and 6) to answer the following questions:

a. are the solutions relatively similar or are they totally different?

b. if they are different, how are they different?

c. given that all three IVPs were very similar, would you expect this behavior in the solutions?

8) use matlab to plot all three of your solutions (found in parts 1), 3), and 5)) on the same plot and each over -1x1 and 0.98y1.02

9) we are looking at IVPs, compare the three solutions in the plot created in part 8) to answer the following questions. (note the scale on your graph from part 8))

a. are the solutions relatively similar in this region near the inital conditions or are they totally different in this region near the initial conditions?

b. given that all three IVPs were very similar, would you expect this behavior in the solutions?