61.24.46 problem 46

Internal problem ID [12459]
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 : 46
Date solved : Tuesday, January 28, 2025 at 03:11:16 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -13\right )}{26 x^{4}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-1/13*a*(6*x-13)*x^(-5/2)*y(x)=-1/26*a^2*(x-1)*(x-13)*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]-1/13*a*(6*x-13)*x^(-5/2)*y[x]==-1/26*a^2*(x-1)*(x-13)*x^(-4),y[x],x,IncludeSingularSolutions -> True]
 

Not solved