How to solve equality and multiple inequality constraints at the same time?

How can I solve the equations and plot x1 vs t.

%Initial conditions
x1=14; x2=14; x3=14;
%Equations
x1 =t*x1+x2+t*x3;
x2 = 2*t*x1+t*x2+x3;
x3 = t*x1+x2+t*x3;
% Inequality constraints
5<x1<20;
5<x2<20;
5<x3<20;

Answer 1

[Walter Roberson]

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;
    ]

eqns = 

sol3_partial = solve(eqns(end), x3)

sol3_partial = 

eqns2 = subs(eqns(1:end-1), x3, sol3_partial)

eqns2 = 

sol2_partial = solve(eqns2(1), x2)

sol2_partial = 

eqns3 = subs(eqns2(2:end), x2, sol2_partial)

eqns3 = 

sol1_partial = solve(eqns3(1), x1)

sol1_partial = 

eqns4 = subs(eqns3(2:end), x1, sol1_partial)

eqns4 = 

simplify(eqns4)

ans = 

sol1 = subs(sol1_partial, t, [0;5/2])

sol1 = 

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})

sol2 = 

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)

Answer 2

[Rakshith G]

How can i solve this inequality function:

x1^2 + 2*x2^2 + 3*x3^2 <= 1

x1, x2, x3 >= 0

Need to find all the values of x1, x2 and x3