फलन z = tan-1 \(\frac{y}{x}\) के लिए निम्न कथनों पर विचार कीजिए:

\({S_1} \equiv x\frac{{\partial z}}{{\partial x}} + y\frac{{\partial z}}{{\partial y}} = 0\)

\({S_2} \equiv {x^2}\frac{{{\partial ^2}z}}{{\partial {x^2}}} + 2xy\frac{{{\partial ^2}z}}{{\partial x\partial y}} + {y^2}\frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\)

\({S_3} \equiv \frac{{{\partial ^2}z}}{{\partial {x^2}}} + \frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\)

कौन सा/से कथन सत्य है/हैं?