MATLAB: Unable to find symbolic solution warning

ode'ssolve

% Define function names that I wish to solve 
syms x(t) y(t);
k1 = 0.02;
k2 = 0.00004;
k3 = 0.0004;
k4 = 0.04;
ode1 = diff(x) == k1*x-k2*x*y;
ode2 = diff(y) == k3*x*y-k4*y;
odes = [ode1;ode2];
S = dsolve(odes);

I keep getting a warning when I'm trying to solve this very simple system of odes.

Best Answer

It is nonllinear because of the ‘x*y’ terms, so it does not have an analytic solution that the Symbolic Math Toolbox can solve for.

Likely the only way to solve it is to use odeToVectorField and matlabFunction functions to create an anonymous function to use with the numeric ODE solvers, such as ode45 or ode15s:

[VF,Sbs] = odeToVectorField(odes);
odsefcn = matlabFunction(VF, 'Vars',{T,Y});

Related Solutions

MATLAB: Solve second order ode system numerically

I would normally expect this to work for other systems of differential equations:

syms k1 k2 k3 k4 k5 k6 k7 k8 u x(t) y(t) Y 
Dx = diff(x);
D2x = diff(Dx);
Dy = diff(y);
D2y = diff(Dy);
Eqn1 = k1*Dx + k2*Dy + k3*x + k4*y == u;
Eqn2 = k5*D2x + k6*D2y + k7*Dy + k8*y == 0;
[VF,Subs] = odeToVectorField(Eqn1, Eqn2)
odeFcn = matlabFunction(VF, 'Vars',{t, Y, u, [k1, k2, k3, k4, k5, k6, k7, k8]})

However, that code throws this error:

Error using mupadengine/feval (line 187)
Number of indeterminates exceeds the number of ODEs.

I must leave it to you to resolve that problem.

MATLAB: ODE solver: Undefined function or variable ‘y’

The problem is here:

syms u(t) v(t)
ode1 = diff(x) == 0.25*x - 0.002*x.^2 - 0.005*x*y;
ode2 = diff(y) == 0.05*y - 0.009*y.^2 - 0.005*x*y;

You need to re-define ‘ode1’ and ‘ode2’ in terms of ‘u’ and ‘v’. The Symbolic Math Toolbox requires that the variables be declared first, before you use them in your code.

Best Answer

Related Solutions

MATLAB: Solve second order ode system numerically

MATLAB: ODE solver: Undefined function or variable ‘y’

Related Question