61.24.49 problem 49

Internal problem ID [12462]
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 : 49
Date solved : Tuesday, January 28, 2025 at 03:13:06 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-\frac {6 a \left (4 x +1\right ) y}{5 x^{{7}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{{9}/{5}}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-6/5*a*(4*x+1)*x^(-7/5)*y(x)=1/5*a^2*(x-1)*(27*x+8)*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]-6/5*a*(4*x+1)*x^(-7/5)*y[x]==1/5*a^2*(x-1)*(27*x+8)*x^(-9/5),y[x],x,IncludeSingularSolutions -> True]
 

Timed out