> with(DEtools):
with(plots):
> DE01:=diff(y(t),t)=t-y(t)^2;
(1)
First, we plot the direction field and some isoclines:
> A1:=DEplot(DE01,y(t),t=-3..3,y=-3..3): #The direction
> A2:=implicitplot(t-y^2=0,t=-3..3,y=-3..3,color=black):
for y'=0
A3:=implicitplot(t-y^2=1,t=-3..3,y=-3..3,color=black):
for y'=1
A4:=implicitplot(t-y^2=-2,t=-3..3,y=-3..3,color=black):
for y'=-2
field
#Isocline
#Isocline
#Isocline
> display(A1,A2,A3,A4); #Display the plots (overlaying them all)
> DEplot(DE01,y(t),t=-3..3,y=-3..3,[[y(0)=1],[y(-1)=0],[y(1)=1]],
linecolor=black); > dsolve(DE01,y(t));
(2)
> ?AiryAi