Exams › GATE › Engineering Mathematics

The type of partial differential equation ∂²P/∂x² + ∂²P/∂y² + 3 ∂²P/∂x∂y + 2 ∂P/∂x - ∂P/∂y = 0 is

1. elliptic
2. parabolic
3. hyperbolic
4. none of these

Correct answer: hyperbolic

Solution

The equation is classified as hyperbolic because it can be transformed into a canonical form that exhibits characteristics of wave propagation, typically indicated by the presence of mixed derivative terms and the appropriate sign conditions in the second-order derivatives.

Related GATE Engineering Mathematics questions

• The second-order differential equation in an unknown function u: u(x,y) is defined as ∂²u/∂x² = 2. Assuming g: g(x), f: f(y), and h: h(y), the general solution of the above differential equation is
• Which of the following equations belong/belongs to the class of second-order, linear, homogeneous partial differential equations:
• The solution of the equation x dy/dx + y = 0 passing through the point (1,1) is
• The Laplace transform F(s) of the exponential function, f(t)=e^(at) when t≥0, where a is a constant and (s−a)>0, is
• The Laplace transform of sinh(at) is
• An ordinary differential equation is given below. (dy/dx)(x ln x) = y The solution for the above equation is (Note: K denotes a constant in the options)

⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →