Teaching MPPSC Assistant Professor Mock Test Series 2025 Engineering Mathematics Differential Equations Partial Differential Equations
The solution of \(z = {\left( {\frac{{\partial z}}{{\partial x}}} \right)^2} + {\left( {\frac{{\partial z}}{{\partial y}}} \right)^2}\) will be
1
\(z = \frac{{{{\left( {x + ay} \right)}^2}}}{{4\left( {1 + {a^2}} \right)}} + b\) where a and b are arbitrary constants.
2
\(z = \frac{{{{\left( {x - ay} \right)}^2}}}{{4\left( {1 + {a^2}} \right)}} + b\) where a and b are arbitrary constants.
3
\(z = \frac{{{{\left( {x - ay} \right)}^2}}}{{4\left( {1 - {a^2}} \right)}} + b\) where a and b are arbitrary constants.
4
\(z = \frac{{{{\left( {x + ay} \right)}^2}}}{{4\left( {1 - {a^2}} \right)}} + b\) where a and b are arbitrary constants.