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View Equation

The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.4. Other Second-Order Equations
Equation(s):\noindent
$\displaystyle \frac{\partial^2w}{\partial t\partial x} = \left (\frac{\partial w}{\partial t}+aw\right )\frac{\partial^2w}{\partial x^2}\left ( \frac{\partial w}{\partial x} \right )^{-1} -a \frac{\partial w}{\partial x}+f(x)\left ( \frac{\partial w}{\partial t}+a w\right )$.

%\noindent
%$\displaystyle \frac{\partial^2w}{\partial t\partial x} = \left (\frac{\partial w}{\partial t}+aw\right )\frac{\partial^2w}{\partial x^2}\left ( \frac{\partial w}{\partial x} \right )^{-1} -a \frac{\partial w}{\partial x}+B(x)\left ( \frac{\partial w}{\partial x}+a w\right )$,\hfill\break
%where $a$ is a constant, $B(x)$ is a function.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
General solution:\hfill\break
$\displaystyle w(t,x) = e^{-at}\Phi\left(\Psi(t)+\int\,\exp\left [-\int\,f(x)\,dx\right ]\,dx \right)$,\hfill\break
where $\Psi(t)$ and $\Phi(z)$ are arbitray functions.

%\noindent
%The general solution:\hfill\break
%$\displaystyle w(t,x) = G\left \{F(t)+\int\,\exp\left [-\int\,B(x)\,dx\right ]\,dx \right \}e^{-at}$,\hfill\break
%where $F(t)$ and $G(z)$ are arbitray functions.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Kosovtsov
First name:Yurii
Country:Ukraine
City:Lvov
Statistic information
Submission date:Wed 13 Dec 2006 11:02
Edits by author:1
Last edit by author:Wed 16 Jan 2008 09:37

Edit (Only for author/contributor)


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