Teaching CSIR NET Mock Test Series Mathematical Science Partial Differential Equations Laplace Equation, Heat and Wave Equations
The following partial differential equation
\(x^2 \frac{\partial^2 u}{\partial x^2}+ x y \frac{\partial^2 u}{\partial x \partial y}\) - \(2 y^2 \frac{\partial^2 u}{\partial y^2}+\frac{\partial u}{\partial x}+2\frac{\partial u}{\partial y}=0\)
is
1
elliptic for x > 0, y ≤ 0
2
parabolic for x > 0, y > 0
3
hyperbolic for x < 0, y < 0
4
hyperbolic for x = 0 y > 0