Yes, 'dsolve' gives general solution as well as solution for horizontal asymptotes.
you can use 'fplot' function to plot solution of differential equation.
>> syms y(t)
>> sol = dsolve(diff(y,t) == y^2 - 24*y + 140)
>> fplot(unique(subs(sol,"C1",[-3:3,(-3:3)+pi*1i])))