Internal problem ID [10012]
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. Equations of
the form \(y y'=f_1(x) y+f_0(x)\)
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {3 y^{\prime } y-\frac {\left (-7 \lambda s \left (3 s +4 \lambda \right ) x +6 s -2 \lambda \right ) y}{x^{\frac {1}{3}}}-\frac {6 \left (\lambda s x -1\right )}{x^{\frac {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^{\frac {1}{3}}=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[3*y[x]*y'[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