Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Partial Differential Equations Laplace Equation, Heat and Wave Equations
Which of the following partial differential equations is NOT PARABOLIC for all \(x, y\in \mathbb{R}\)?
1
\({x^2}\frac{{{\partial ^2}u}}{{\partial x\partial y}} +4xy\frac{{\partial u}}{{\partial y}} + {y^2} = 0\)
2
\({x^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} - 2xy\frac{{{\partial ^2}u}}{{\partial x\partial y}} + {y^2}\frac{{{\partial ^2}u}}{{\partial {y^2}}} = 0\)
3
\({x^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} + 2xy\frac{{{\partial ^2}u}}{{\partial x\partial y}} + {y^2}\frac{{{\partial ^2}u}}{{\partial {y^2}}} = 0\)
4
\(2{x^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} - 4xy\frac{{{\partial ^2}u}}{{\partial x\partial y}} + 2{y^2}\frac{{{\partial ^2}u}}{{\partial {y^2}}} + x\frac{{\partial u}}{{\partial x}} + y\frac{{\partial u}}{{\partial y}} = 0\)
5
Question Not Attempted