MiniLogo

EqWorld

The World of Mathematical Equations

IPM Logo

Exact Solutions Methods Software For Authors Math Forums

EqArchive: Add Equation/Solution > View Equation

 English only

View Equation

The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.2. Second-Order Quasilinear Hyperbolic Equations
Equation(s):\noindent
$\displaystyle \frac{\partial^2 w}{\partial t \, \partial x}  = w \frac{\partial^2 w}{\partial t^2 }$
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
The general solution:\hfill\break
$\displaystyle  w(t,x) = \int_c^{\Phi}\xi\,F(\xi)\,e^{x\xi}\,d\xi+\frac{dG(x)}{dx}$,\hfill\break
where $\Phi=\Phi(t,x)$ is a solution of the following equation

$\displaystyle  t+\int_c^{\Phi}F(\xi)\,e^{x\xi}\,d\xi+G(x)=0$,\hfill\break


and $F(\xi)$ and $G(x)$ are arbitrary functions, and $c$ is an arbitrary constant.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Kosovtsov
First name:Yurii
Country:Ukraine
City:Lvov
Statistic information
Submission date:Mon 16 Jul 2007 10:00
Edits by author:2
Last edit by author:Tue 03 Feb 2009 11:05

Edit (Only for author/contributor)


The EqWorld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations.

Copyright © 2006-2011 Andrei D. Polyanin, Alexei I. Zhurov and Alexander L. Levitin