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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):$\displaystyle \frac{\partial ^2w}{\partial t^2}+at^b\frac{\partial^mw}{\partial x^m}=0$,\hfill\break
where $b\neq-2;\ b\neq-2\pm\frac 1k; \ k=1,2,3,...$
Solution(s),
Transformation(s),
Integral(s)
:
1. Particular solutions:\hfill\break
$w_0(x,t)=1$,\\
$w_1(x,t)=x$,\\
$w_2(x,t)=x^2$,\\
$...$,\\
$\displaystyle w_n(x,t)=x^n+\sum_{k=1}^{n-mk\geq0} 
\frac {(-a)^kn!t^{kb+2k}x^{n-mk}}{(n-mk)!k!(b+2)^{2k}\left(\frac{b+1}{b+2}\right)_k}$.

2. Particular solutions:\hfill\break
$w_0(x,t)=t$,\\
$w_1(x,t)=xt$,\\
$w_2(x,t)=x^2t$,\\
$...$,\\
$\displaystyle w_n(x,t)=x^nt+\sum_{k=1}^{n-mk\geq0} 
\frac {(-a)^kn!t^{kb+2k+1}x^{n-mk}}{(n-mk)!k!(b+2)^{2k}\left(\frac{b+3}{b+2}\right)_k}$.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Stepuchev
First name:Valeriy
Country:Latvija
City:Sigulda
Statistic information
Submission date:Thu 09 Sep 2010 18:56
Edits by author:1
Last edit by author:Thu 08 Oct 2015 18:29

Edit (Only for author/contributor)


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