55.22.52 problem 52

Internal problem ID [13593]
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 : 52
Date solved : Sunday, October 12, 2025 at 04:02:19 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 4014

ode:=y(x)*diff(y(x),x)-y(x) = -12/49*x+1/49*A*(5*x^(1/2)+262*A+65*A^2/x^(1/2)); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-28/121*x+2/121*A*(5*x^(1/2)+262*A+65*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") 
y = Function("y") 
ode = Eq(-A*(65*A**2/sqrt(x) + 262*A + 5*sqrt(x))/49 + 12*x/49 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out