Consider a spherical wave formed from a disturbance at the center of a shallow pool. At time \(t=0\) a small, steady, stream of droplets begins hitting the pool. They cause a disturbance of amplitude, \(\delta_{o}\), with slope 0 at the center that spreads out in all directions. This disturbance results in conditions at the center so that the slope, height, and speed of the wave remain constant there.

a. Derive the differential equation describing the wave propagation for an infinite pool of depth, \(h_{o}\).

b. Convert the differential equation to pseudo-Cartesian coordinates by forming a new height variable, \(\eta=r \delta_{\lambda}\). Solve the differential equation for the wave height, \(\delta_{\lambda}\).