simple pendulum equation, why it cannot be solved with laplace transform (the general solution)

Question

Usually to solve the simple pendulum equation: $\qquad \ell {\ddot \theta }+g\sin \theta =0\,$

Using the first term of Taylor series is used as approximation, but although $\sin \theta$ can be transformed to Laplace "space" and use it to find a general solution, I can't find it.

Why there is no general solution in Laplace?

Answer 1

In general, Laplace transform can be helpful in solving linear differential equations. But this one is nonlinear.