error: 'Inputs must be floats, namely single or double' while trying to solve an ODE having an unknown coefficient.

I am trying to solve the given problem using ode45.

x'' + a x' + 7.9( x^3) = 3.2 sin(xt), and x(0) = 1.2, x'(0) = −3.3, and x(2.3) = −0.6

In this i have to find possible values of a for which x(2.3)=-0.6

Now i am trying to get a symbolic expression in a for which x(2.3) = f(a)

from this i will get an expression for a which can be solved to get possible possible values of a for which f(a) = -0.6.

Now i have written a matlab code to get this expression but matlab returns an error 'Inputs must be floats, namely single or double'

i am not sure whether ode45 can be used to get an expression for x(t) containg an unknown a. Please suggest the changes in the code below

this is the first .m file:

function pdot=func4(t,q)
pdot=sym(zeros(size(q)));
syms a;
pdot(1)=q(2);
pdot(2)=3.2*sin(q(1)*t)-a*q(2)-7.9*((q(1))^3);
end

second .m file

x0=[1.2 -3.3];
tspan=0:0.1:2.5;
opts = odeset('RelTol',1e-12,'AbsTol',1e-12);
[t,x]=ode45('func4',tspan,x0,opts);
fprintf(x(:,1));

after running the second .m file i get this error

Error using odearguments (line 113)

Inputs must be floats, namely single or double.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in odeforty_five (line 4)

[t,x]=ode45('func4',tspan,x0,opts);

Answer 1

[Walter Roberson]

The function you call for ode*() is permitted to use symbolic expressions internally, but the return value must be completely numeric. Even returning a sym form of a number is not permitted: only double or single.

ode45 is completely numeric and cannot be used to return a symbolic expression.

You will need to use a completely different approach.

Potentially dsolve() might work for you... but probably not.

If dsolve() does not work for you then you have a Boundary Value Problem and should use bvp4c or similar routines.

[ASHU JAGLAN]

Thank you for your response

dsolve is not working in this case.The given problem has to be solved using ode45 command only

Can something else be tried in this case?

[Walter Roberson]

It is not possible to solve this task using ode45 command only. It is potentially possible to solve it using ode45 and "the shooting method" (basically, a binary search). See http://www.mathworks.com/help/matlab/math/parameterizing-functions.html for how you can pass a trial numeric a value into the function.