Consider the following equations
\[\begin{gathered} \frac{{\partial {\text{V}}\left( {{\text{x, y}}} \right)}}{{\partial {\text{x}}}} = {\text{p}}{{\text{x}}^2} + {{\text{y}}^2} + 2{\text{xy}} \hfill \\ \frac{{\partial {\text{V}}\left( {{\text{x, y}}} \right)}}{{\partial {\text{y}}}} = {{\text{x}}^2} + {\text{q}}{{\text{y}}^2} + 2{\text{xy}} \hfill \\ \end{gathered} \]
where p and q are constants. V(x, y) that satisfies the above equations is

A. \[{\text{p}}\frac{{{{\text{x}}^3}}}{3} + {\text{q}}\frac{{{{\text{y}}^3}}}{3} + 2{\text{xy}} + 6\]

B. \[{\text{p}}\frac{{{{\text{x}}^3}}}{3} + {\text{q}}\frac{{{{\text{y}}^3}}}{3} + 5\]

C. \[{\text{p}}\frac{{{{\text{x}}^3}}}{3} + {\text{q}}\frac{{{{\text{y}}^3}}}{3} + {{\text{x}}^2}{\text{y}} + {\text{x}}{{\text{y}}^2} + {\text{xy}}\]

D. \[{\text{p}}\frac{{{{\text{x}}^3}}}{3} + {\text{q}}\frac{{{{\text{y}}^3}}}{3} + {{\text{x}}^2}{\text{y}} + {\text{x}}{{\text{y}}^2}\]

Answer: Option D