GATE Civil 2024 Set 1 | Question: 18

Question

​​​​​​For the following partial differential equation,

\[
x \frac{\partial^{2} f}{\partial x^{2}}+y \frac{\partial^{2} f}{\partial y^{2}}=\frac{x^{2}+y^{2}}{2}
\]
which of the following option(s) is/are CORRECT?

• A. elliptic for $x>0$ and $y>0$
• B. parabolic for $x>0$ and $y>0$
• C. elliptic for $x=0$ and $y>0$
• D. hyperbolic for $x<0$ and $y>0$