syms x1 x2 x3 t
x10 = 14; x20 = 14; x30 = 14; x0 = [x10,x20,x30];
eqns = [
x1 == t*x1+x2+t*x3
x2 == 2*t*x1+t*x2+x3;
x3 == t*x1+x2+t*x3;
x1 + x2 + x3 == 42;
]
sol3_partial = solve(eqns(end), x3)
eqns2 = subs(eqns(1:end-1), x3, sol3_partial)
sol2_partial = solve(eqns2(1), x2)
eqns3 = subs(eqns2(2:end), x2, sol2_partial)
sol1_partial = solve(eqns3(1), x1)
eqns4 = subs(eqns3(2:end), x1, sol1_partial)
simplify(eqns4)
sol1 = subs(sol1_partial, t, [0;5/2])
We can see from that the 5/2 version does not satisfy the range constraints for x1
sol2 = subs(sol2_partial, {t, x1}, {0, 14})
and using the equality constraint, we quickly deduce that x3 must be 14 as well.
So the only solution is [14, 14, 14] at time 0
(My internal reference for this is T0098941)
