Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Partial Differential Equations
Consider the second-order partial differential equation (PDE)
\(\frac{\partial^2 u}{\partial x^2}+4 \frac{\partial^2 u}{\partial x \partial y}\) + \(\left(x^2+4 y^2\right) \frac{\partial^2 u}{\partial y^2}\) = sin(x + y).
Consider the following statements
P: The PDE is parabolic on the ellipse \(\frac{x^2}{4}+y^2=1\).
Q: The PDE is hyperbolic inside the ellipse \(\frac{x^2}{4}+y^2=1\).
Then
1
both P and Q are TRUE
2
P is TRUE and Q is FALSE
3
P is FALSE and Q is TRUE
4
both P and Q are FALSE
5
Question Not Attempted