Math Lab #4
(a) - [2 points] Use the Maple command DEplot to construct the slope field of the ordinary differential equation y' = (1- t2 )/(1+ y2 ) on the rectangle t = -1..2, y = -3..3.
(b) -[3 points] Use the Maple command DEplot to plot the solutions of the given o.d.e.
that satisfy the following initial conditions:
y(0) = -1, y(0) = -.5, y(0) = 0, y(0) = .5, y(0) =1 .
(c) - [3 points] Use the Maple command implicitplot to plot the isoclines of the given o.d.e. along which the slope of any solution is c for the following values: .2, .4, .6, .8. Isoclines are curves of constant slope in the t-y plane. If y' = f(t, y) then the curve of constant slope c is given by the equation f(t, y) = c.
(d) - [2 points] Use the Maple command display to combine the results of (a), (b) and (c).