How can i find P function which i have x and y derivatives.

My question is numerical

dP/dx=[0    3.82   8.1;  0    3.59    7.74 ;  0    2.82    6.53]   
dP/dy=[-1  -1 -1;-4.82  -5.05  -5.64; -8.19  -8.74  -10.14]

d^2P/dx^2+d^2P/dy^2=0

How can i find P as matrix.

Finite difference method i tried but i failed.

[Walter Roberson]

integrate dP/dx with respect to x and dP/dy with respect to y, and add them.

The result would be a 3x3 P that is constant * x + constant times y... you can skip the explicit integration because it is so simple.

The derivative of each entry with respect to x would be just its x coefficient.

The derivative of each entry with respect to y would be its y coefficients.

With dx and dy being constant their derivatives would be 0, and the sum of two zeros is zero so the second derivative conditions are met.