61.25.3 problem 3

Internal problem ID [12417]
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 1.3.4-2.
Problem number : 3
Date solved : Wednesday, March 05, 2025 at 07:03:44 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y+a k \,x^{2}+b x +c \right ) y^{\prime }&=-a y^{2}+2 a k x y+m y+k \left (k +b -m \right ) x +s \end{align*}

✗ Maple

ode:=(y(x)+a*k*x^2+b*x+c)*diff(y(x),x) = -y(x)^2*a+2*a*k*x*y(x)+m*y(x)+k*(k+b-m)*x+s; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(y[x]+a*k*x^2+b*x+c)*D[y[x],x]==-a*y[x]^2+2*a*k*x*y[x]+m*y[x]+k*(k+b-m)*x+s; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
k = symbols("k") 
m = symbols("m") 
s = symbols("s") 
y = Function("y") 
ode = Eq(-2*a*k*x*y(x) + a*y(x)**2 - k*x*(b + k - m) - m*y(x) - s + (a*k*x**2 + b*x + c + y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out