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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):$\displaystyle
\frac{\partial^2 w}{\partial x^2}=
\left( {\alpha y + \beta } \right)^\gamma \frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial y^2},
\qquad \gamma\ne1$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:
$$
w(x,y) = \frac{{A^2 }}{{12}}x^4  + \frac{{AB}}{3}x^3  + \frac{{B^2
}}{2}x^2  + ax + b - \left( {Ax + B} \right) \left(\frac{{3 -
\gamma }}{{\sqrt {2\alpha ^3 (1 - \gamma )} }}\left( {\alpha y +
\beta } \right)^{\frac{{3 - \gamma }}{2}} + C\right).
$$
where $A$, $B$, and $C$ are arbitrary constants.
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 12:40
Edits by author:0

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