How can I solve This system of ODEs?

I tried to solve these ODE equations but there is an error!

This is my code:

 syms x1(w) x2(w)  x3(w)  
T=773.15; R=1.314;  
K=(3.35e+24)*exp(-(70e+3)/(1.987*T)); 
Keq=exp(53.47-(27330/T));

 ode1=diff(x1,w)==((-K*x1)/((x1+x2+x3)*(R*T))*(1-((x2*x3^3)/(x1*((x1+x2+x3)^3)*Keq))));

 ode2=diff(x2,w)==((K*x1)/((x1+x2+x3)*(R*T))*(1-((x2*x3^3)/(x1*((x1+x2+x3)^3)*Keq))));

 ode3=diff(x3,w)==((3*K*x1)/((x1+x2+x3)*(R*T))*(1-((x2*x3^3)/(x1*((x1+x2+x3)^3)*Keq))));

 odes=[ode1;ode2;ode3]

 cond1=x1(0)==2;
 cond2=x2(0)==0;
 cond3=x3(0)==4;

 conds=[cond1;cond2;cond3];

 [x1Sol(w), x2Sol(w),  x3Sol(w)] = dsolve(odes,conds)

And this is the error message

 Warning: Explicit solution could not be found. 
> In dsolve (line 201) 
Error using sym/subsindex (line 796)
Invalid indexing or function definition. When defining a function, ensure that the arguments are symbolic variables and
the body of the function is a SYM expression. When indexing, the input must be numeric, logical, or ':'.

Answer 1

[Star Strider]

You can create a function usable in the numeric ODE solvers by adding:

[odes_vf, vfsubs] = odeToVectorField(odes);
odes_fcn = matlabFunction(odes_vf, 'Vars',{w, Y});

[w,y] = ode15s(odes_fcn, [0 1], [2; 0; 4]);

just after your ‘odes’ assignment. However when I tried that, the numerical integration threw warnings and produced nothing.

Answer 2

[Karan Gill]

You have numeric values in your equations, so solve this numerically. Try ode45: https://www.mathworks.com/help/matlab/ref/ode45.html

For the difference between symbolic and numeric methods, see: https://www.mathworks.com/help/symbolic/choose-symbolic-or-numeric-arithmetic.html.

The error is because you didn't declare the symbolic functions [x1Sol(w), x2Sol(w), x3Sol(w)]. You can ignore it for the moment and focus on getting a solution.