t1_prob4_ANS_A10.mws
Mon Oct 10 09:45:25 MDT 2005

A Maple solution to problem 4, Test #1.

The problem was to sketch the , , and  isoclines, the direction field, and the  solution

for the differential equation y' = t - y^2 + 2.

>

restart;

>	with(plots, display, implicitplot, textplot);

>	with(DEtools, DEplot);

############################################################

Plot ranges, the RHS function, and the list of slopes:

>	TRG := -5..4: YRG := -3..3:

>	RHS := (t,y) -> t - y^2 + 2;

>	mLIST := [-1,0,1]; Slopes for isoclines

######################################

Here's a Maple procedure which, given the slope , produces a labeled plot of the corresponding isocline.

>

utah := proc(u)   slope -> labeled isocline  local tm, ym, us;  tm := op(2, TRG);  ym := sort(evalf([solve(RHS(tm,y)=u,y)]))[2];  us := convert(u, 'string'):  us := "m = "||us:  implicitplot(RHS(t,y)=u, t=TRG, y=YRG,        colour=BLACK,grid=[75,75]),    textplot([tm+1/5,ym, us], align={ABOVE,RIGHT}): end;

##############################################################

Now "map" and "utah" generate the list of plots of labeled isoclines.

>	isoclineLIST := map(utah, mLIST): Plots of isoclines

>	P := op(isoclineLIST):

#############################################################

Now we set up the differential equation and the y(-1) = -1 initial condition to plot the direction field and the solution curve.

>	DE := D(y)(t) = RHS(t, y(t));

>	VAR := y(t):

>	INIT := [[y(-1)=-1]]:

>	P := P, DEplot(DE,VAR,t=TRG,INIT,y=YRG, stepsize=0.05):

###############################################################

Produce a plot with isoclines, direction field, and the solution curve:

>	display([P]);

>	#######################################

>