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I'm working with static beams with Euler–Bernoulli model which ODE is $$ \dfrac{d^2}{dx^2} \left(EI \cdot \dfrac{d^2w}{dx^2}\right) = q(x). $$ With a beam along the $x$ axis, the solution consists of ...

At the Wikipedia there are the differential formulation for Euler-Bernoulli Beam \eqref{1} and Timoshenko Beam \eqref{2} $$ \begin{align} &\dfrac{d^2}{dx^2}\left(EI\dfrac{d^2w}{dx^2}\right) = q(x) ...