55.22.47 problem 47

Internal problem ID [13588]
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 : 47
Date solved : Wednesday, October 01, 2025 at 06:14:29 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=12 x +\frac {A}{x^{{5}/{2}}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 110

ode:=y(x)*diff(y(x),x)-y(x) = 12*x+A/x^(5/2); 
dsolve(ode,y(x), singsol=all);
 

\[ c_1 +\frac {12 \left (2^{{2}/{3}} \left (\frac {3 x^{{3}/{2}} y^{2}}{4}-6 y x^{{5}/{2}}+A +12 x^{{7}/{2}}\right ) \left (\frac {48 x^{{7}/{2}}-24 y x^{{5}/{2}}+3 x^{{3}/{2}} y^{2}+4 A}{A}\right )^{{1}/{6}}-56 \operatorname {hypergeom}\left (\left [-\frac {1}{6}, \frac {1}{2}\right ], \left [\frac {3}{2}\right ], -\frac {3 x^{{3}/{2}} \left (-4 x +y\right )^{2}}{4 A}\right ) x^{{5}/{2}} \left (x -\frac {y}{4}\right )\right ) \sqrt {3}}{\sqrt {-A \,x^{{7}/{2}}}} = 0 \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==12*x+A*x^(-5/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
y = Function("y") 
ode = Eq(-A/x**(5/2) - 12*x + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out