60.1.245 problem 250

Internal problem ID [10259]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 250
Date solved : Sunday, March 30, 2025 at 03:34:58 PM
CAS classification : [[_Abel, `2nd type`, `class B`]]

\begin{align*} \left (B x y+A \,x^{2}+a x +b y+c \right ) y^{\prime }-B g \left (x \right )^{2}+A x y+\alpha x +\beta y+\gamma &=0 \end{align*}

✗ Maple

ode:=(B*x*y(x)+A*x^2+a*x+b*y(x)+c)*diff(y(x),x)-B*g(x)^2+A*x*y(x)+alpha*x+beta*y(x)+gamma = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(B*x*y[x]+A*x^2+a*x+b*y[x]+c)*D[y[x],x]-B*g[x]^2+A*x*y[x]+\[Alpha]*x+\[Beta]*y[x]+\[Gamma]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
Alpha = symbols("Alpha") 
B = symbols("B") 
BETA = symbols("BETA") 
Gamma = symbols("Gamma") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(A*x*y(x) + Alpha*x - B*g(x)**2 + BETA*y(x) + Gamma + (A*x**2 + B*x*y(x) + a*x + b*y(x) + c)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out