55.24.58 problem 58

Internal problem ID [13687]
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 : Thursday, October 02, 2025 at 12:59:42 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }-\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*}

✗ Maple

ode:=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); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=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); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
k = symbols("k") 
y = Function("y") 
ode = Eq(-a**2*x**(1 - 2*k)*(2*k - 3)*(x - 1)**2/2 - a*(-4*k + x*(4*k - 7) + 5)*y(x)/(2*x**k) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out