Question: When a shaft rotates with angular velocity ω the displacement y at a distance x from one end due to centrifugal force is given by the equation:

\[\frac{{{d}^{4}}y}{d\,{{x}^{4}}}={{n}^{4}}y\ \,where\,\,{{n}^{4}}=\frac{W{{\omega }^{2}}}{gEI}\]

Show that the equation is satisfied by:

Where A, B, C, and D are constants.