55.22.49 problem 49

Internal problem ID [13590]
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 : 49
Date solved : Sunday, October 12, 2025 at 04:00:47 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 196

ode:=y(x)*diff(y(x),x)-y(x) = 2*x+2*A*(10*x^(1/2)+31*A+30*A^2/x^(1/2)); 
dsolve(ode,y(x), singsol=all);
 

\[ c_1 -\frac {\left (\sqrt {x}+3 A \right ) 2^{{1}/{3}} \left (\frac {12 A^{2}+10 \sqrt {x}\, A +2 x -y}{6 A^{2}+2 \sqrt {x}\, A +y}\right )^{{1}/{3}} \left (\frac {15 A^{2}+8 \sqrt {x}\, A +x +y}{6 A^{2}+2 \sqrt {x}\, A +y}\right )^{{1}/{6}} y}{4 \sqrt {\frac {\left (\sqrt {x}+3 A \right )^{2}}{6 A^{2}+2 \sqrt {x}\, A +y}}\, \left (6 A^{2}+2 \sqrt {x}\, A +y\right ) A}-\int _{}^{\frac {6 \sqrt {x}\, A +2 x -3 y}{12 A^{2}+4 \sqrt {x}\, A +2 y}}\frac {\left (\textit {\_a} +1\right )^{{1}/{3}} \left (2 \textit {\_a} +5\right )^{{1}/{6}}}{\sqrt {2 \textit {\_a} +3}}d \textit {\_a} = 0 \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==2*x+2*A*(10*x^(1/2)+31*A+30*A^2*x^(-1/2)); 
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(-2*A*(30*A**2/sqrt(x) + 31*A + 10*sqrt(x)) - 2*x + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out