61.24.24 problem 24

Internal problem ID [12437]
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 : 24
Date solved : Tuesday, January 28, 2025 at 03:06:11 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)+1/15*a*(13*x-18)*x^(-7/5)*y(x)=-4/15*a^2*(x-1)*(x-6)*x^(-9/5),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]+1/15*a*(13*x-18)*x^(-7/5)*y[x]==-4/15*a^2*(x-1)*(x-6)*x^(-9/5),y[x],x,IncludeSingularSolutions -> True]
 

Timed out