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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):$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^{\!2}-\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}
=f(w)\left(\frac{\partial w}{\partial x}\right)^{\!4}$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent 1. Exact solution:\hfill\break
$\displaystyle x-y\int\sqrt{f(w)}\,dw=\varphi(w)$,\hfill\break
where $\varphi(w)$ is an arbitrary function.
\medskip

\noindent 2. Exact solution:\hfill\break
$\displaystyle x+y\int\sqrt{f(w)}\,dw&=\psi(w)$,\hfill\break
where $\psi(w)$ is an arbitrary function.
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:Wed 06 Dec 2006 11:32
Edits by author:0

Edit (Only for author/contributor)


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