Internal problem ID [9919]
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. Form \(y y'-y=f(x)\). subsection 1.3.1-2. Solvable
equations and their solutions
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime } y-y-\frac {\left (2 m +1\right ) x}{4 m^{2}}-\frac {A}{x}+\frac {A^{2}}{x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 165
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)
\[ c_{1}+\frac {-\left (\int _{}^{-\frac {x^{2}}{2 x y \relax (x )+2 A}}\frac {\left (-m +\textit {\_a} \right )^{\frac {1}{m +1}} \left (\left (1+2 m \right ) \textit {\_a} +m \right )^{\frac {1+2 m}{m +1}}}{\textit {\_a}^{2}}d \textit {\_a} \right ) A x +\left (\frac {\left (-2 x^{2}+2 x y \relax (x )+2 A \right ) m -x^{2}}{x y \relax (x )+A}\right )^{\frac {1+2 m}{m +1}} y \relax (x ) 2^{-\frac {m}{m +1}} \left (\frac {-2 y \relax (x ) m x -2 A m -x^{2}}{2 x y \relax (x )+2 A}\right )^{\frac {1}{m +1}} \left (x y \relax (x )+A \right )}{x} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[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