61.24.30 problem 30

Internal problem ID [12443]
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 : 30
Date solved : Tuesday, January 28, 2025 at 03:08:01 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y+\frac {3 a \left (3 x +11\right ) y}{14 x^{{10}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -27\right )}{14 x^{{13}/{7}}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)+3/14*a*(3*x+11)*x^(-10/7)*y(x)=-1/14*a^2*(x-1)*(x-27)*x^(-13/7),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]+3/14*a*(3*x+11)*x^(-10/7)*y[x]==-1/14*a^2*(x-1)*(x-27)*x^(-13/7),y[x],x,IncludeSingularSolutions -> True]
 

Timed out