Example: how to solve first-order quasi-linear equations in Maple with PDEplot
Taken from the book by Belzer(?)

> with(PDEtools,PDEplot):

> alias( u=u(x,t) ):

> PDE := diff(u,t) + u*diff(u,x) = 0;

[Maple Math]

> initdata := [s,0,1-s^2]:

> PDEplot(PDE, u, initdata, s=-1..1, x=-1..3, t=0..2.5, orientation=[-110,60], axes=box, style=hidden, shading=none);

> plots[display](%, orientation=[110,60] );

>

>