Vibrating Beam. In studying the transverse vibrations of a

QUESTION:

Vibrating Beam. In studying the transverse vibrations of a beam, one encounters the homogeneous equation where y(x) is related to the displacement of the beam at position x, the constant E is Young’s modulus, I is the area moment of inertia, and k is a parameter. Assuming E, I, and k are positive constants, find a general solution in terms of sines, cosines, hyperbolic sines, and hyperbolic cosines.