The problem has nothing to do with the ODE solver, it is because of how you defined your function like this:
function dydt = first_order_conversion_two_eqn(t,V)
But then nowhere inside that function do you define a variable called dydt. If you want to return the variable dydt then you need to define what it is:
function dydt = first_order_conversion_two_eqn(t,V)
...
dydt = ???
end
However your function has other problems: you never use the input arguments, so calling the ODE solver might not be doing what you expect it to do, and the load call (which is very slow) should be moved outside the function and the data passed as a third input argument:
S = load(...);
fun = @(t,y)@first_order_conversion_two_eqn(t,y,S);
[t,V] = ode15s(fun, tspan, y0)
where the function has been changed to have three inputs:
function dydt = first_order_conversion_two_eqn(t,y,S)
