55.24.53 problem 53

Internal problem ID [13682]
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 : 53
Date solved : Sunday, October 12, 2025 at 04:31:31 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 156

ode:=y(x)*diff(y(x),x)+1/5*a*(x-6)/x^(7/5)*y(x) = 2/5*a^2*(x-1)*(x+4)/x^(9/5); 
dsolve(ode,y(x), singsol=all);
 

\[ c_1 -\frac {80 \sqrt {3}\, \left (a y x^{{2}/{5}}+\frac {x^{{4}/{5}} y^{2}}{8}+\frac {a \left (y x^{{7}/{5}}-2 a \left (x +24\right ) \left (x -1\right )\right )}{24}\right ) \left (a y x^{{2}/{5}}+\frac {x^{{4}/{5}} y^{2}}{8}+\frac {a \left (y x^{{7}/{5}}+\frac {a \left (x +4\right )^{2}}{2}\right )}{4}\right ) \sqrt {\frac {-y x^{{2}/{5}}-a x +a}{x^{{2}/{5}} \left (y+x^{{3}/{5}} a \right )}}}{9 \left (\frac {a}{x^{{2}/{5}} \left (y+x^{{3}/{5}} a \right )}\right )^{{5}/{2}} \left (y x^{{2}/{5}}+a x \right )^{2} x \left (y x^{{2}/{5}}+a \left (x +4\right )\right )^{2}} = 0 \]

✗ Mathematica

ode=y[x]*D[y[x],x]+1/5*a*(x-6)*x^(-7/5)*y[x]==2/5*a^2*(x-1)*(x+4)*x^(-9/5); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-2*a**2*(x - 1)*(x + 4)/(5*x**(9/5)) + a*(x - 6)*y(x)/(5*x**(7/5)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out