55.24.36 problem 36

Internal problem ID [13665]
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 : 36
Date solved : Sunday, October 12, 2025 at 04:24:13 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 167

ode:=y(x)*diff(y(x),x)-a*(5*x-4)/x^4*y(x) = a^2*(x-1)*(3*x-1)/x^7; 
dsolve(ode,y(x), singsol=all);
 

\[ c_1 -\frac {9 \,5^{{1}/{6}} 2^{{2}/{3}} \sqrt {\frac {x^{3} y+a x -a}{\left (x^{2} y+a \right ) x}}\, \left (x -\frac {3}{4}\right )}{5 x {\left (-\frac {a}{x \left (x^{2} y+a \right )}\right )}^{{1}/{3}} \left (\frac {3 x^{3} y+3 a x -a}{\left (x^{2} y+a \right ) x}\right )^{{1}/{6}}}-729 \int _{}^{\frac {\frac {9 x^{3} y}{5}+\frac {9 a x}{5}-\frac {27 a}{20}}{\left (x^{2} y+a \right ) x}}\frac {\textit {\_a} \sqrt {20 \textit {\_a} -9}}{\left (5 \textit {\_a} -9\right )^{{1}/{3}} \left (4 \textit {\_a} +9\right )^{{1}/{6}} \left (400 \textit {\_a}^{3}-1701 \textit {\_a} +729\right )}d \textit {\_a} = 0 \]

✗ Mathematica

ode=y[x]*D[y[x],x]-a*(5*x-4)*x^(-4)*y[x]==a^2*(x-1)*(3*x-1)*x^(-7); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out