61.22.12 problem 12

Internal problem ID [12258]
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 : 12
Date solved : Monday, March 31, 2025 at 04:55:57 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=\frac {2 m -2}{\left (m -3\right )^{2}}+\frac {2 A \left (m \left (m +3\right ) \sqrt {x}+\left (4 m^{2}+3 m +9\right ) A +\frac {3 m \left (m +3\right ) A^{2}}{\sqrt {x}}\right )}{\left (m -3\right )^{2}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = 2*(m-1)/(m-3)^2+2*A/(m-3)^2*(m*(3+m)*x^(1/2)+(4*m^2+3*m+9)*A+3*m*(3+m)*A^2/x^(1/2)); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==2*(m-1)/(m-3)^2+2*A/(m-3)^2*(m*(m+3)*x^(1/2)+(4*m^2+3*m+9)*A+3*m*(m+3)*A^2*x^(-1/2)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
m = symbols("m") 
y = Function("y") 
ode = Eq(-2*A*(3*A**2*m*(m + 3)/sqrt(x) + A*(4*m**2 + 3*m + 9) + m*sqrt(x)*(m + 3))/(m - 3)**2 + y(x)*Derivative(y(x), x) - y(x) - (2*m - 2)/(m - 3)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out