61.24.58 problem 58

Internal problem ID [12471]
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 : 58
Date solved : Tuesday, January 28, 2025 at 03:14:11 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✗ Solution by Maple

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

Not solved