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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:3.1. Second-Order Parabolic Equations
Equation(s):$\displaystyle a^2t \frac{\partial w}{\partial t}+\frac{\partial^2w}{\partial x^2}=0$.
Solution(s),
Transformation(s),
Integral(s)
:
1. Partucular solutions:\hfill\break
$w_0(x,t)=1$,\\
$w_1(x,t)=t\cos(ax)$,\\
$w_2(x,t)=t^2\cos(\sqrt{2}\,ax)$,\\
$w_3(x,t)=t^3\cos(\sqrt{3}\,ax)$,\\
$w_4(x,t)=t^4\cos(\sqrt{4}\,ax)$,\\
$\dots$,\\
$w_n(x,t)=t^n\cos(\sqrt{n}\,ax)$.
\medskip

2. Partucular solutions:\\
$w_0(x,t)=x$,\\
$w_1(x,t)=t\sin(ax)$,\\
$w_2(x,t)=t^2\sin(\sqrt{2}\,ax)$,\\
$w_3(x,t)=t^3\sin(\sqrt{3}\,ax)$,\\
$w_4(x,t)=t^4\sin(\sqrt{4}\,ax)$,\\
$\dots$,\\
$w_n(x,t)=t^n\sin(\sqrt{n}\,ax)$.
Novelty:New solution(s) / integral(s)
Author/Contributor's Details
Last name:Stepuchev
First name:Valeriy
Country:Latvija
City:Sigulda
Statistic information
Submission date:Sun 18 May 2008 06:57
Edits by author:1
Last edit by author:Mon 23 Feb 2009 13:45

Edit (Only for author/contributor)


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