61.22.22 problem 22

Internal problem ID [12268]
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 1.3.1-2. Solvable equations and their solutions
Problem number : 22
Date solved : Monday, March 31, 2025 at 04:57:58 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A}{\sqrt {x}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 189

ode:=y(x)*diff(y(x),x)-y(x) = -4/25*x+A/x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ c_1 +\frac {31250 \left (-\frac {y^{5}}{10}+A^{2} y^{2}\right ) x^{{3}/{2}}+62500 \left (\frac {y^{4}}{5}-2 A^{2} y\right ) x^{{5}/{2}}+20000 \left (-y^{3}+4 A^{2}\right ) x^{{7}/{2}}-16000 A \,x^{5}+60000 A y x^{4}-75000 A y^{2} x^{3}+31250 A y^{3} x^{2}-125000 A^{3} x^{2}+16000 y^{2} x^{{9}/{2}}-6400 y x^{{11}/{2}}+1024 x^{{13}/{2}}}{\sqrt {x^{{3}/{2}} A}\, x^{{3}/{2}} A \left (25 \sqrt {x}\, A -4 \left (x -\frac {5 y}{4}\right )^{2}\right ) \left (\frac {100 \sqrt {x}\, A -16 x^{2}+40 x y-25 y^{2}}{\sqrt {x}\, A}\right )^{{3}/{2}}} = 0 \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-4/25*x+A*x^(-1/2); 
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/sqrt(x) + 4*x/25 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out