Discussion
The governing equation for the static transverse deflection of a beam under an uniformly distributed load, according to Euler-Bernoulli (engineering) beam theory, is a
Answer: B
The equation is a 4th order linear non-homogenous ordinary differential equation.
Euler-Bernoulli theory gives the static deflection \(w(x)\) of a beam under a distributed load \(q(x)\) as
\[ EI\,\frac{d^{4}w}{dx^{4}} = q(x) \]
It has one independent variable, so it is ordinary, not partial. The highest derivative is the fourth. The unknown and its derivatives appear only to the first power, so it is linear, and the load term on the right makes it non-homogeneous.
The 2nd order form \(EI\,w'' = M(x)\) is written in terms of the bending moment, not the load, and the equation is neither nonlinear nor homogeneous under a uniformly distributed load.
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