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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:3.2. Second-Order Hyperbolic Equations
Equation(s):$\displaystyle \frac{\partial^2w}{\partial t^2}=a\frac{\partial ^2w}{\partial x^2}+b\frac{\partial ^2w}{\partial y^2}$.
Solution(s),
Transformation(s),
Integral(s)
:
Particular solutions:\\
$\displaystyle w_{m,n}(t,x,y)=\sum^{m-2k\geq0}_{k=0}\sum^{n-2j\geq0}_{j=0}{\frac{(k+j)!a^kb^jt^{2k+2j}x^{m-2k}y^{n-2j}}{k!j!(2k+2j)!(m-2k)!(n-2j)!}}$,\\
$\displaystyle w_{m,n}(t,x,y)=\sum^{m-2k\geq0}_{k=0}\sum^{n-2j\geq0}_{j=0}{\frac{(k+j)!a^kb^jt^{2k+2j+1}x^{m-2k}y^{n-2j}}{k!j!(2k+2j+1)!(m-2k)!(n-2j)!}}$,\\
where $m,\,n=0,\,1,\,2,\,\dots$
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 20 May 2008 20:43
Edits by author:0

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