55.24.18 problem 18

Internal problem ID [13647]
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 1.3.3-2.
Problem number : 18
Date solved : Wednesday, October 01, 2025 at 10:44:21 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 y y^{\prime }&=\frac {\left (-7 \lambda s \left (3 s +4 \lambda \right ) x +6 s -2 \lambda \right ) y}{x^{{1}/{3}}}+\frac {6 \lambda s x -6}{x^{{2}/{3}}}+2 \left (\lambda s \left (3 s +4 \lambda \right ) x +5 \lambda \right ) \left (-\lambda s \left (3 s +4 \lambda \right ) x +3 s +4 \lambda \right ) x^{{1}/{3}} \end{align*}

✗ Maple

ode:=3*y(x)*diff(y(x),x) = (-7*lambda*s*(3*s+4*lambda)*x+6*s-2*lambda)/x^(1/3)*y(x)+6*(lambda*s*x-1)/x^(2/3)+2*(lambda*s*(3*s+4*lambda)*x+5*lambda)*(-lambda*s*(3*s+4*lambda)*x+3*s+4*lambda)*x^(1/3); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=3*y[x]*D[y[x],x]==(-7*\[Lambda]*s*(3*s+4*\[Lambda])*x+6*s-2*\[Lambda])*x^(-1/3)*y[x]+6*(\[Lambda]*s*x-1)*x^(-2/3)+2*(\[Lambda]*s*(3*s+4*\[Lambda])*x+5*\[Lambda])*(-\[Lambda]*s*(3*s+4*\[Lambda])*x+3*s+4*\[Lambda])*x^(1/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
lambda_ = symbols("lambda_") 
s = symbols("s") 
y = Function("y") 
ode = Eq(-x**(1/3)*(2*lambda_*s*x*(4*lambda_ + 3*s) + 10*lambda_)*(-lambda_*s*x*(4*lambda_ + 3*s) + 4*lambda_ + 3*s) + 3*y(x)*Derivative(y(x), x) - (-7*lambda_*s*x*(4*lambda_ + 3*s) - 2*lambda_ + 6*s)*y(x)/x**(1/3) - (6*lambda_*s*x - 6)/x**(2/3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out