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View Equation

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

Equation data
Category:2. First-Order Partial Differential Equations
Subcategory:2.1. Linear Equations
Equation(s):$\displaystyle 
x_2 \frac{\partial u}{\partial x_1}+
2 x_3 \frac{\partial u}{\partial x_2}+
3 x_4 \frac{\partial u}{\partial x_3}+
\frac{1}{6} (30 x_4 x_1+20 x_3 x_2+10 x_2 x_1^3-20 x_3 x_1^2-15 x_2^2 x_1-x_1^5) 
\frac{\partial u}{\partial x_4}=0
$\hfill\break
Solution(s),
Transformation(s),
Integral(s)
:
Particular solutions:\hfill\break
$\displaystyle u_1&=\frac{2 q_2 q_4-q_3^2}{q_4^2}$,\hfill\break
$\displaystyle u_2&=\frac{2 x_1 q_3-q_2^2+2 q_4}{q_4^2}$,\hfill\break
$\displaystyle u_3&=\frac{x_1 q_4^2-q_2 q_3 q_4+q_3^3/3}{q_4^3}$,\hfill\break

where

$\displaystyle q_2=x_2-x_1^2 $,\hfill\break
$\displaystyle q_3=2 x_3-3 x_2 x_1+x_1^3 $,\hfill\break
$\displaystyle q_4=6 x_4-8 x_3 x_1-3x_2^2+6 x_2 x_1^2-x_1^4 $.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Kirichenko
First name:Vladimir
Country:Russia
Statistic information
Submission date:Fri 18 Dec 2009 17:46
Edits by author:0

Edit (Only for author/contributor)


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