restart;

kernelopts(version);

with(inttrans):

exp(-a*t);

laplace(%, t, s);

invlaplace(%, s, t);

restart;

kernelopts(version);

with(plots):

setoptions3d(font=[Times,roman,12]);

arrow(<1,1,1>);

restart;

v := (x,t) -> piecewise(x <= -t, 0, x < t, 1 - 1/2*(1 - x/t));

de := diff(x(t),t) = v(x(t),t);

ic := x(0) = -a;

x__exact := t -> piecewise(t < a, -a, t - 2*sqrt(t)*sqrt(a));

a := 3;  # any a>0 should do
dsol := dsolve({de,ic}, numeric):
plots:-odeplot(dsol, t=0..5);   # dsolve solution
plot(x__exact(t), t=0..5);      # symbolic solution (calculated by hand)
a := 'a';

dsolve({de, ic}) assuming a > 0, t > 0;

restart;

doit := proc(a, b, n::posint)
        local p := 1, L := [ [a], [b] ];
        for p from 1 to n-1 do
                 L := [ map( x -> [a,op(x)], L)[], map( x -> [b,op(x)], L)[] ];
        end do:
        return L;
end proc:

doit(a,b,1);

doit(p,q,3);

doit(5,7,3);