[40 points] The steady-state height of water in a one-dimensional, unconfined groundwater aquifer (as shown in...

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[40 points] The steady-state height of water in a one-dimensional, unconfined groundwater aquifer (as shown in Figure 1) can be modeled with the nonlinear ODE d dx (Khd) + N = 0, (1) where x is the distance (m), K is hydraulic conductivity (m/d), h is the height of the water table (m), and N is infiltration rate (m/d). Given the domain and conditions x = 0 to 1000m with h(0) 10 m, h(1000) = 5m, K = 1m/d, and N = 0.0001 m/d: Ground surface Water table 1 Infiltration 1111111 Aquifer Groundwater flow Confining bed Figure 1: An unconfined groundwater aquifer a) Solve for the water height using the shooting method (use scipy.integrate.solve_ivp to integrate). b) Solve for the water height using the finite-difference method (Ax = 10 m). Hint: for both parts, apply the product rule to the outer derivative. == [40 points] The steady-state height of water in a one-dimensional, unconfined groundwater aquifer (as shown in Figure 1) can be modeled with the nonlinear ODE d dx (Khd) + N = 0, (1) where x is the distance (m), K is hydraulic conductivity (m/d), h is the height of the water table (m), and N is infiltration rate (m/d). Given the domain and conditions x = 0 to 1000m with h(0) 10 m, h(1000) = 5m, K = 1m/d, and N = 0.0001 m/d: Ground surface Water table 1 Infiltration 1111111 Aquifer Groundwater flow Confining bed Figure 1: An unconfined groundwater aquifer a) Solve for the water height using the shooting method (use scipy.integrate.solve_ivp to integrate). b) Solve for the water height using the finite-difference method (Ax = 10 m). Hint: for both parts, apply the product rule to the outer derivative. ==