61.24.26 problem 26

Internal problem ID [12439]
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 : 26
Date solved : Tuesday, January 28, 2025 at 03:06:23 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y+\frac {3 a \left (19 x -14\right ) x^{{7}/{5}} y}{35}&=-\frac {4 a^{2} \left (x -1\right ) \left (9 x -14\right ) x^{{9}/{5}}}{35} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)+3/35*a*(19*x-14)*x^(7/5)*y(x)=-4/35*a^2*(x-1)*(9*x-14)*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]+3/35*a*(19*x-14)*x^(7/5)*y[x]==-4/35*a^2*(x-1)*(9*x-14)*x^(9/5),y[x],x,IncludeSingularSolutions -> True]
 

Timed out