A linearized groundwater model was used to simulate the height of the water table for an unconfined aquifer. A more realistic result can be obtained by using the following nonlinear ODE:

Where x = distance (m), K = hydraulic conductivity (m/d), h = height of the water table (m), and N = infiltration rate (m/d). Solve for the height of the water table for the same case as in Prob. 28.30. That is solve from x = 0 to 1000 m with h(0) = 10 m, h(1000) 5 = m, K = 1 m/d, and N = 0.0001 m/d. Obtain your solution with
(a) The shooting method and
(b) The finite-difference method.

dh Kh,)+ N = 0 dx, dx