61.24.23 problem 23

Internal problem ID [12436]
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 : 23
Date solved : Tuesday, January 28, 2025 at 03:05:47 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y+\frac {a \left (19 x +85\right ) y}{26 x^{{18}/{13}}}&=-\frac {3 a^{2} \left (x -1\right ) \left (x +25\right )}{26 x^{{23}/{13}}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)+1/26*a*(19*x+85)*x^(-18/13)*y(x)=-3/26*a^2*(x-1)*(x+25)*x^(-23/13),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]+1/26*a*(19*x+85)*x^(-18/13)*y[x]==-3/26*a^2*(x-1)*(x+25)*x^(-23/13),y[x],x,IncludeSingularSolutions -> True]
 

Timed out