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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):$\displaystyle\frac{\partial^2 w}{\partial x^2}  = (\alpha y + \beta) \frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial y^2}$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:
$$
\begin{array}{l} \vspace{0.1cm}
 w(x,y) = \dfrac{{A^2 }}{{12}}x^4  + \dfrac{{AB}}{3}x^3  + \dfrac{{B^2 }}{2}x^2  + ax + b +  \\
  + \left( {Ax + B} \right)\left\{ {C_1  + \sqrt {\dfrac{2}{{\alpha ^3 }}} \left( {\alpha y + \beta }
  \right)\sum\limits_{n = 1}^\infty  {\left( { - 1} \right)^{n + 1} \dfrac{{2^n }}{{\left( {2n + 1} \right)!!}}}
  \left[ {\ln \left( {\alpha y + \beta } \right)} \right]^{\frac{{2n + 1}}{2}} }
  \right\}.
 \end{array}
$$
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 12:42
Edits by author:0

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