Next consider the initial value problem

1. (a)

y =y2 t, y(0)=c, for t[0,5].

Use dfield (Java version) or ndfield8 (Matlab version) to plot the direction field of the differential equation with the Display window set for 0 t 5 and 3 y 3. Set the window properties to use arrows when displaying the direction field. Print out your plot.

(b) Use dfield (Java version) or dfield8 (Matlab version) to plot solutions of the initial value problem for 0 c 1 with increment of 0.1. Show that there exists a value P such that if c < P then the solution eventually decreases, while if c > P the solution always increases.

2. Use forward Eulers method with step size h = 0.05, h = 0.1 and h = 0.2 to find approximate values of the solution on the interval 0 t 5 for c = P + 0.01 and c = P 0.01.