61.24.34 problem 34

Internal problem ID [12447]
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 : 34
Date solved : Tuesday, January 28, 2025 at 03:09:04 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}}&=-\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)+1/6*a*(13*x-3)*x^(-2/3)*y(x)=-1/6*a^2*(x-1)*(5*x-1)*x^(-1/3),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]+1/6*a*(13*x-3)*x^(-2/3)*y[x]==-1/6*a^2*(x-1)*(5*x-1)*x^(-1/3),y[x],x,IncludeSingularSolutions -> True]
 

Not solved