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View Equation

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

Equation data
Category:1. Ordinary Differential Equations
Subcategory:1.3. Second-Order Nonlinear Equations
Equation(s):$\displaystyle x^{2}y_{xx}^{\prime \prime }=axy_{x}^{\prime }+by+c\left( y_{x}^{\prime
}\right) ^{k}$,\hfill\break
where $a,b,c,k\neq 0$ and $k\neq 1$.
Solution(s),
Transformation(s),
Integral(s)
:
Particular solution:\hfill\break
$\displaystyle y\left( x\right) =\left\{ \frac{1}{c}\left( \frac{k-1}{k}\right) ^{k}\left[ 
\frac{k}{\left( k-1\right) ^{2}}-b\frac{k}{k-1}-a\right] \right\} ^{\frac{1}{%
k-1}}x^{\frac{k}{k-1}}$,\hfill\break
where $a\neq \frac{k}{\left( k-1\right) ^{2}}-b\frac{k}{k-1}$.
Novelty:New equation(s) & solution(s) & transformation(s)
Author/Contributor's Details
Last name:Koulovatianos
First name:Christos
Country:United kingdom
City:Nottingham
Affiliation:University of Nottingham
Statistic information
Submission date:Fri 25 May 2012 11:13
Edits by author:0

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