MiniLogo

EqWorld

The World of Mathematical Equations

IPM Logo

Exact Solutions Methods Software For Authors Math Forums

EqArchive: Add Equation/Solution > View Equation

 English only

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
$\displaystyle \left(\frac{\partial w}{\partial t}+a\right)\frac{\partial^2 w}{\partial t\partial x}
-\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial t^2} 
+\frac{\partial w}{\partial x}\left[2\left(\frac{\partial w}{\partial t}\right)^2+3a \frac{\partial w}{\partial t}+a^2 \right]=0$.

%\noindent
%$\displaystyle \left(\frac{\partial w}{\partial t}+a\right)\frac{\partial^2 w}{\partial t\partial x} +\frac{\partial w}{\partial x}\left[2\left(\frac{\partial w}{\partial t}\right)^2+3a \frac{\partial w}{\partial t}-\frac{\partial^2 w}{\partial t^2}+a^2 \right]=0$,\hfill\break
%where $a$ is a constant.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
The general solution in implicit form:\hfill\break
$\displaystyle e^{at+2w}+F(at+w)e^{at+w}+G(x) = 0$,\hfill\break
where $F(z)$ and $G(x)$ are arbitrary functions.

%\noindent
%The general solution in implicit form:\hfill\break
%$\displaystyle \left[\exp(w(t,x))\right]^2 e^{at}+F[a t+w(t,x)]\exp(w(t,x))e^{at}+G(x) = 0$,\hfill\break
%where $F$ and $G$ are arbitrary 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:Tue 12 Dec 2006 12:13
Edits by author:0

Edit (Only for author/contributor)


The EqWorld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations.

Copyright © 2006-2011 Andrei D. Polyanin, Alexei I. Zhurov and Alexander L. Levitin