>    deq:=diff(v(t),t)=g+a/m(t)-diff(m(t),t)/m(t)*v(t);

deq := diff(v(t),t) = g+a/m(t)-diff(m(t),t)/m(t)*v(t)

>    m(t):=4*(R0+c*t)^3*Pi/3*rho;

m(t) := 4/3*(R0+c*t)^3*Pi*rho

>    a:=-alpha*abs(v(t))*v(t);

a := -alpha*abs(v(t))*v(t)

>    g:=10; R0:=0.001; c:=R0/10; rho:=1000; alpha:=1e-6; deq;

g := 10

R0 := .1e-2

c := .1000000000e-3

rho := 1000

alpha := .1e-5

diff(v(t),t) = 10-.7500000000e-9*abs(v(t))*v(t)/(.1e-2+.1000000000e-3*t)^3/Pi-.3000000000e-3/(.1e-2+.1000000000e-3*t)*v(t)

>    with(DEtools):

>    DEplot(deq,v(t),t=0..4,v=-2..14,[[v(0)=-2],[v(0)=2],[v(0)=6],[v(0)=10],[v(0)=14]],stepsize=0.1,colour=black,linecolor=[blue,yellow,black,red,green]);

[Maple Plot]

>