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:3. Linear Partial Differential Equations
Subcategory:3.5. Higher-Order Equations
Equation(s):$\displaystyle \frac{\partial ^3w}{\partial t^3}+
a\frac{\partial^mw}{\partial x^m}=0$.
Solution(s),
Transformation(s),
Integral(s)
:
1. Particular solutions:\\
$w_0(x,t)=1$,\\
$w_1(x,t)=x$,\\
$...$,\\
$\displaystyle w_n(x,t)=x^n+
\sum_{k=1}^{n-mk\geq0} \frac {(-a)^kn!t^{3k}x^{n-mk}}{(n-mk)!(3k)!}$.

2. Particular solutions:\\
$w_0(x,t)=t$,\\
$w_1(x,t)=xt$,\\
$...$,\\
$\displaystyle w_n(x,t)=x^nt+\sum_{k=1}^{n-mk\geq0} 
\frac {(-a)^kn!t^{3k+1}x^{n-mk}}{(n-mk)!(3k+1)!}$.

3. Particular solutions:\\
$w_0(x,t)=t^2$,\\
$w_1(x,t)=xt^2$,\\
$...$,\\
$\displaystyle w_n(x,t)=x^nt^2+\sum_{k=1}^{n-mk\geq0} 
\frac {(-a)^kn!t^{3k+2}x^{n-mk}}{(n-mk)!(3k+2)!}.
Novelty:New solution(s) / integral(s)
Author/Contributor's Details
Last name:Stepuchev
First name:Valeriy
Country:Latvija
City:Sigulda
Statistic information
Submission date:Tue 14 Sep 2010 19:33
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