Warning: Explicit solution could not be found

EDU>> syms sim_phi(t)
Dy = diff(sim_phi);
sim_phi(t) = dsolve(diff(sim_phi, t, t) == -9.8*sim_phi);
sim_phi(t) = simplify(sim_phi)

syms phi(t)
Dy = diff(phi);
phi(t) = dsolve(diff(phi, t, t) == -9.8*sin(phi));
phi(t) = simplify(phi)

sim_phi(t) =

C2*cos((7*5^(1/2)*t)/5) + C3*sin((7*5^(1/2)*t)/5)

Warning: Explicit solution could not be found; implicit solution returned. 
> In dsolve at 204 

phi(t) =

                                                                                                                       0
   solve(C22 - t + int((2^(1/2)*i)/(2*(C20 - (49*cos(phi))/5)^(1/2)), phi, 'IgnoreAnalyticConstraints', true) == 0, phi)
   solve(C22 - t - int((2^(1/2)*i)/(2*(C20 - (49*cos(phi))/5)^(1/2)), phi, 'IgnoreAnalyticConstraints', true) == 0, phi

So I am attempting to solve the differential for a pendulum, with and without using the small angle approximation of sin(theta) ~= theta. I am getting the warning in the dsolve for the part without the small angle approximation.

The ultimate goal of my project is to compare values for t for theta<<1 and theta>1.

If this is not doable through matlab, there are other projects I can work on. It's for a class, and our assignment is to "Do any math/science problem that you want to solve and present using Matlab"

I only have the tools available in the $99 student version of Matlab. R2014a...

MATLAB and Simulink Student Suite

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Answer 1

[Alan Weiss]

Instead of trying to solve the ODE analytically (I mean symbolically), I suggest that you solve it numerically using an ODE solver.

Alan Weiss

MATLAB mathematical toolbox documentation