61.22.63 problem 63

Internal problem ID [12309]
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 : 63
Date solved : Wednesday, March 05, 2025 at 06:36:37 PM
CAS classification : [[_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==k*(A*x^2+B*x+c)^(-1/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out