[t,x] = ode45(@odefcn,tspan,[0 0]);
That is valid syntax.
However, your function is relying on the variables a, b, c, and u. MATLAB never automatically passes variables from the calling environment into a function. If you define
x = 42;
y = f();
and you have defined
function result = f(x)
result = x.^2;
end
then when you call f without passing any argument into it, MATLAB does not look and see that the internal parameter name for the first argument is x and then look into the script and see there is an x there and use the caller's x as the value for x in the function. That never happens for named parameters. (There are cases where MATLAB will look for a variable in an outer environment, but that is never done for named parameters.)
So... at the time that your function odefcn first needs to use a, b, c, or u, the function would fail, because you would not have passed the values into the function.
The approach you used with the anonymous function
@(t,x) odefcn(t, x, a, b, c, u)
is the recommended approach. http://www.mathworks.com/help/matlab/math/parameterizing-functions.html
The approach Alan suggested, of instead passing extra parameters, has not been documented since about MATLAB 5.2 or so, and has some subtle internal incompatibilities so it is not completely reliable.
