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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):$\displaystyle w\left(\frac{\partial^2 w}{\partial x\partial y}\right)^2+
\left(\frac{\partial w}{\partial x}\right)^2\frac{\partial^2 w}{\partial y^2}+
f(y)\left(\frac{\partial w}{\partial x}\right)^2\frac{\partial w}{\partial y}=0$.\hfill\break
Solution(s),
Transformation(s),
Integral(s)
:
Solutions:
$$
w=C\int\left[\exp\left(-\int f(y)\,dy\right)\right]+\Phi(x),
$$
$$
w=\sqrt{C\int\left[\exp\left(-\int f(y)\,dy\right)\right]+\Phi(x)},
$$
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 
(http://eqworld.ipmnet.ru\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
Country:Russia
City:Saint-Petersburg
Statistic information
Submission date:Wed 09 Jan 2008 14:06
Edits by author:0

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