A general solution of the partial differential equation \(\dfrac{\partial^{2} f(x, y)}{\partial x^{2}} - \dfrac{\partial^{2} f(x, y)}{\partial y^{2}} = 0\) can be expressed in terms of arbitrary functions \(u\) and \(v\) as:
\(f(x, y) = u(x + y) + v(x - y)\)
The equation \(\partial^{2} f/\partial x^{2} - \partial^{2} f/\partial y^{2} = 0\) is the one dimensional wave-type equation, which factorises as \(\left(\partial_x - \partial_y\right)\left(\partial_x + \partial_y\right) f = 0\).
Introducing characteristic coordinates \(\xi = x + y\) and \(\eta = x - y\), the equation becomes \(\partial^{2} f/\partial \xi\, \partial \eta = 0\), whose general solution is a sum of an arbitrary function of \(\xi\) and an arbitrary function of \(\eta\).
Hence, \(f(x, y) = u(x + y) + v(x - y)\).
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Important Questions from Mixed Topic (MH-SET)
.................... is a client server application that identifies each host on the internet with a unique user-friendly name.
Every OS has a ................ or .......... which primarily resides in the main memory of the computer to perform some of the basic functions of the OS.
(i) Kernel
(ii) Interface
(iii) Nucleus
(iv) Compiler
Codes:
Which of the following are referred to as low level language?
(i) Machine language
(ii) Assembly language
(iii) High level language
(iv) Natural language
Codes:
Match the following:
List I List II (a) New York Public Library (i) Shelv AR (b) Miami University Augmented Research Group (ii) Smart library (c) Oula University Library (iii) Wolf Walk (d) North Carolina State University (iv) Find the future Codes:
Which part of the QR code represents the encoded data?
