Error with Invalid indexing in system of differential equations

I want to solve an ODE and getting this error message:

Error using sym/subsindex (line 953)

Invalid indexing or function definition. Indexing must follow MATLAB indexing.

Function arguments must be symbolic variables, and function body must be sym

expression.

Error in kinetik_3 (line 28)

[sSol(t),eSol(t),cSol(t),pSol(t)] = dsolve(odes);

k1 = 1.0;
k2 = 0.8;
k3 = 1.1;

syms s(t) e(t) c(t) p(t) 

ode1 = diff(s) == -k1*s*e + k2*c;
ode2 = diff(e) == -k1*s*e + k2*c + k3*c;
ode3 = diff(c) == k1*s*e - k2*c - k3*c;
ode4 = diff(p) == k3*c;

odes = [ode1; ode2; ode3; ode4];

cond1 = s(0) == 2.9;
cond2 = e(0) == 1.3;
cond3 = c(0) == 0;
cond4 = p(0) == 0;

conds = [cond1; cond2; cond3; cond4];

[sSol(t),eSol(t),cSol(t),pSol(t)] = dsolve(odes,conds);

Can someone please explain?

Answer 1

[Star Strider]

Remove the ‘(t)’ in the dsolve output and the error disappears. However, the system is nonlinear, so an analytic solution likely does not exist. Numerically integrate it instead.

k1 = 1.0;
k2 = 0.8;
k3 = 1.1;

syms s(t) e(t) c(t) p(t) T Y

ode1 = diff(s) == -k1*s*e + k2*c;
ode2 = diff(e) == -k1*s*e + k2*c + k3*c;
ode3 = diff(c) == k1*s*e - k2*c - k3*c;
ode4 = diff(p) == k3*c;

odes = [ode1; ode2; ode3; ode4];

cond1 = s(0) == 2.9;
cond2 = e(0) == 1.3;
cond3 = c(0) == 0;
cond4 = p(0) == 0;

conds = [cond1; cond2; cond3; cond4];

% [sSol,eSol,cSol,pSol] = dsolve(odes,conds);

[VF,Subs] = odeToVectorField(odes)

VF = 

Subs = 

odesfcn = matlabFunction(VF, 'Vars',{T,Y})

odesfcn = function_handle with value:
    @(T,Y)[Y(3).*(1.9e+1./1.0e+1)-Y(1).*Y(2);Y(3).*(4.0./5.0)-Y(1).*Y(2);Y(3).*(-1.9e+1./1.0e+1)+Y(1).*Y(2);Y(3).*(1.1e+1./1.0e+1)]

ics = [1.3; 2.9; 0; 0];                                         % Initial Conditio9ns Vector (See 'Subs' To Understand The Order)
tspan = linspace(0,20,250);                                     % Time Vector For Integration
[t,y] = ode45(odesfcn, tspan, ics);                             % Integrate

figure
plot(t, y, 'LineWidth',1.5)
grid
legend(string(Subs), 'Location','best')

Change as necessary to get the desired result.

EDIT — (1 Mar 2022 at 22:12)

Changed ‘tspan’ to produce smoother curves.

.

Answer 2

[Davide Masiello]

I think the problem is in the syntax of your last line.

You should simply write

sSol = dsolve(odes,conds);

I run this on MatLab online and it does not throw an error any longer.

But it still cannot find a symbolic solution.