a) Solve the following initial-value problem using one of the analytical techniques we discussed in
class.
y0 = 2xy + 1; y(0) = 0 (1)
(b) Use Octave to plot the slope elds and the particular solution of equation(1). For the plot use
a window size of xmin = 1, xmax = 3, ymin = 1, ymax = 3.
(c) Use Octave to numerically solve (1) using n = 100 and n = 200 points. Create a plot showing the
two numerical solutions and the analytic solution from part(a). For the plot use xmin = 0, xmax = 8.
(d) Type a report using the following outline as a guide:
I. Introduction and Objectives
II. Discussion of the Euler's Method
III. Discussion of Implementation
{ How were the methods implemented?
{ What kind of problems did you encounter while working with the code?
{ How did you overcome these problems?
IV. Discussion of Results
{ e.g. compare Euler's solution with the analytical solution
V. Summary and Conclusion