__Math 306B__**
Math Lab #4**

__Problem #1__:

**(a) -**** **[2 points] Use the Maple command **DEplot **to construct
the slope field of the ordinary differential equation y**' **= (1- t^{2 })/(1+ y^{2 })
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).

________________________________________________________________________________________