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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
$\displaystyle \frac{\partial^2w}{\partial t\partial x}  = \frac{1}{w}\left(\frac{\partial w}{\partial x} +a\right )\frac{\partial w}{\partial t}+bw\frac{\partial w}{\partial x}$.
%where $a$ and $b\neq 0$ are constants.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
General solution:\hfill\break
$\displaystyle w(t,x) = -\frac{1}{b}\frac{\displaystyle \int_{-\infty}^\infty\frac{1}{\omega}\left[F(\omega)ab\exp \left(\frac{abt+\omega^2x}{\omega}\right )+G(\omega)\omega^2\exp \left(\frac{abx+\omega^2t}{\omega}\right )\right ]\,d\omega}{\displaystyle \int_{-\infty}^\infty\left[F(\omega)\exp \left(\frac{abt+\omega^2x}{\omega}\right )+G(\omega)\exp \left(\frac{abx+\omega^2t}{\omega}\right )\right ]\,d\omega}$,\hfill\break
where $F(\omega)$ and $G(\omega)$ are arbitrary functions, and $b\neq 0$.
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 13 Dec 2006 12:17
Edits by author:0

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