Teaching MPPSC Assistant Professor Mock Test Series 2025 Engineering Mathematics Differential Equations
For the function z = tan-1 \(\frac{y}{x}\) consider the following statements :
\({S_1} \equiv x\frac{{\partial z}}{{\partial x}} + y\frac{{\partial z}}{{\partial y}} = 0\)
\({S_2} \equiv {x^2}\frac{{{\partial ^2}z}}{{\partial {x^2}}} + 2xy\frac{{{\partial ^2}z}}{{\partial x\partial y}} + {y^2}\frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\)
\({S_3} \equiv \frac{{{\partial ^2}z}}{{\partial {x^2}}} + \frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\)
Which of the following is true?
1
only S1
2
only S1 and S2
3
All S1, S2, S3
4
None of these