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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:4.4. Other Second-Order Equations
Equation(s):\noindent
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^{\!2}-\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}
=-f(w)\left(\frac{\partial w}{\partial x}\right)^{\!3}\frac{\partial w}{\partial y}$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Solution:\hfill\break
$\displaystyle x-y\left(\frac12\int\sqrt{f(w)}\,dw+C\right)^2=\varphi(w)$,\hfill\break
where $\varphi(w)$ is an arbitrary function and $C$ is an arbitrary constant.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Fri 08 Dec 2006 15:58
Edits by author:0

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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