83.9.11 problem 12

Internal problem ID [21969]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. X at page 57
Problem number : 12
Date solved : Thursday, October 02, 2025 at 08:20:37 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} a x y-b +\left (c x y-d \right ) x y^{\prime }&=0 \end{align*}

✗ Maple

ode:=a*x*y(x)-b+(c*x*y(x)-d)*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(a*x*y[x]-b)+(c*x*y[x]-d)*x*D[y[x],x]==0; 
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") 
d = symbols("d") 
y = Function("y") 
ode = Eq(a*x*y(x) - b + x*(c*x*y(x) - d)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out