from gekko import GEKKO
import numpy as np

m = GEKKO(remote=False)
x10 = 0; x20 = 1
u, x11, x12, x21, x22, dx11, dx12, dx21, dx22 = m.Array(m.Var,9)
u.value = 1; x11.value = 1; x12.value = 1; x21.value = 1; x22.value = 1 

N = np.array([[0.75, -0.25],\
              [1.00,  0.00]])

m.Equations([np.dot(N[0],[dx11, dx12]) == x11 - x10,
             np.dot(N[1],[dx11, dx12]) == x12 - x10,
             np.dot(N[0],[dx21, dx22]) == x21 - x20,
             np.dot(N[1],[dx21, dx22]) == x22 - x20,
             5*dx11 == -x11 + 2*u**2,
             5*dx12 == -x12 + 2*u**2,
             3*dx21 == -x21 + x11**2,
             3*dx22 == -x22 + x12**2,
             x22-5 == 0])

m.solve(disp=False)
print(u[0])
print(x10, x11[0], x12[0])
print(x20, x21[0], x22[0])
print(dx11[0], dx12[0], dx21[0], dx22[0])