61.24.44 problem 44

Internal problem ID [12457]
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 : 44
Date solved : Tuesday, January 28, 2025 at 03:09:52 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (3 x -4\right )}{8 x^{4}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-1/8*a*(x-8)*x^(-5/2)*y(x)=-1/8*a^2*(x-1)*(3*x-4)*x^(-4),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]-1/8*a*(x-8)*x^(-5/2)*y[x]==-1/8*a^2*(x-1)*(3*x-4)*x^(-4),y[x],x,IncludeSingularSolutions -> True]
 

Not solved