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Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.4. Other Second-Order Equations
Equation(s):$\displaystyle a\left(\frac{\partial^2 w}{\partial x\partial y}\right)^2+
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\left[f(x)\frac{\partial w}{\partial x}+f(x)w+
\frac{\partial w}{\partial x}\right]\frac{\partial^2 w}{\partial y^2}+
a\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x\partial y}=0$.\hfill\break
w=e^{x}\left[C\int\exp\left(x-\int f(x)\,dx\right)\,dx+\Phi(y)\right],
where $\Phi$ is an arbitrary function and $C$ is an arbitrary constant.
Remarks:This result was obtained in co-authorship with L.V. Linchuk,
using generalized group analysis. The main idea of the method 
is outlined at EqWorld 
(\slash ru/solutions/interesting.htm, in Russian).
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Zaitsev
First name:Valentin
Middle(s) name:Feodorovich
Statistic information
Submission date:Wed 09 Jan 2008 14:07
Edits by author:0

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