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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. Particular solutions:\\
$w_0(x,t)=1$,\\
$w_1(x,t)=t\cosh(ax)$,\\
$w_2(x,t)=t^2\cosh(\sqrt{2}\,x)$,\\
$w_3(x,t)=t^3\cosh(\sqrt{3}\,x)$,\\
$w_4(x,t)=t^4\cosh(\sqrt{4}\,x)$,\\
$\dots$,\\
$w_n(x,t)=t^n\cosh(\sqrt{n}\,x)$.
\medskip

2. Particular solutions:\\
$w_0(x,t)=x$,\\
$w_1(x,t)=t\sinh(ax)$,\\
$w_2(x,t)=t^2\sinh(\sqrt{2}\,x)$,\\
$w_3(x,t)=t^3\sinh(\sqrt{3}\,x)$,\\
$w_4(x,t)=t^4\sinh(\sqrt{4}\,x)$,\\
$\dots$,\\
$w_n(x,t)=t^n\sinh(\sqrt{n}\,x)$.
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 07:01
Edits by author:0

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