61.22.13 problem 13

Internal problem ID [12338]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.1-2. Solvable equations and their solutions
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 07:54:51 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 166

dsolve(y(x)*diff(y(x),x)-y(x)=(2*m+1)/(4*m^2)*x+A*1/x-A^2*1/(x^3),y(x), singsol=all)
 

\[ \frac {\left (\frac {-2 y m x -2 A m -x^{2}}{2 x y+2 A}\right )^{\frac {1}{m +1}} y 2^{-\frac {m}{m +1}} \left (x y+A \right ) \left (\frac {\left (-1-2 m \right ) x^{2}+2 y m x +2 A m}{x y+A}\right )^{\frac {1+2 m}{m +1}}-x \left (A \left (\int _{}^{-\frac {x^{2}}{2 x y+2 A}}\frac {\left (-m +\textit {\_a} \right )^{\frac {1}{m +1}} \left (\left (2 \textit {\_a} +1\right ) m +\textit {\_a} \right )^{\frac {1+2 m}{m +1}}}{\textit {\_a}^{2}}d \textit {\_a} \right )-c_{1} \right )}{x} = 0 \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[y[x]*D[y[x],x]-y[x]==(2*m+1)/(4*m^2)*x+A*1/x-A^2*1/(x^3),y[x],x,IncludeSingularSolutions -> True]
 

Not solved