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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
$\displaystyle w\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial t \, \partial y}-
w\frac{\partial w}{\partial t}\frac{\partial^2 w}{\partial y ^2}-
a\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y ^2}+
a\frac{\partial w}{\partial y}\frac{\partial^2w}{\partial x\partial y}+
\frac{\partial w}{\partial t}\left(\frac{\partial w}{\partial y}\right)^2=0$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
The general solution in implicit form ($w=w(t,x,y) $):\hfill\break
$\displaystyle yw+\int_c^t G\left(\xi,\,x+\frac{a(\xi-t)}{w}\right)\,d\xi +F(w,xw-at) = 0 ,\\$\hfill\break
where $F$ and $G$ are arbitrary functions of two arguments, $c$ 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:Wed 04 Jul 2007 13:43
Edits by author:0

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