61.24.18 problem 18

Internal problem ID [12431]
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 : Tuesday, January 28, 2025 at 03:02:20 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 y^{\prime } y&=\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*}

✗ Solution by Maple

dsolve(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),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[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),y[x],x,IncludeSingularSolutions -> True]
 

Timed out