MiniLogo

EqWorld

The World of Mathematical Equations

IPM Logo

Exact Solutions Methods Software For Authors Math Forums

EqArchive: Add Equation/Solution > View Equation

 English only

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
\frac{\partial^2 w}{\partial x^2} = f(y)\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial y^2}.
$
Solution(s),
Transformation(s),
Integral(s)
:
1. Solution:
$$
w(x,y) = \frac{{A^2 }}{{12}}x^4  + \frac{{AB}}{3}x^3  + \frac{{B^2
}}{2}x^2  + ax + b + \left( {Ax + B} \right)\int {\left( {\int
{\frac{{2 dy}}{{f(y)}}} } \right)} ^{1/2} dy,
$$
where $A$ and $B$ are arbitrary constants.
\medskip

2. Solution:
$$
w(x,y) = Ax + B + C_1\left( {C_2 - \dfrac{x}{{\sqrt 6 }}}
\right)^{ - 2} \varphi (y),
$$
where $A$, $B$, $C_1$, and $C_2$ are arbitrary constants, and 
function $\varphi (y)$ is described by ordinary differential equation
$$
f(y)\varphi '_y \varphi ''_{yy}  = \varphi.
$$
Remarks:Here $f(y)$ in an arbitrary function.
Novelty:New equation(s) & solution(s) & transformation(s)
Author/Contributor's Details
Last name:Vyazmina
First name:Elena
Country:Russia
City:Moscow
Affiliation:Institute for Problems in Mechanics
Statistic information
Submission date:Fri 25 Jan 2008 12:37
Edits by author:0

Edit (Only for author/contributor)


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