23.1.513 problem 503

Internal problem ID [5120]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 503
Date solved : Tuesday, September 30, 2025 at 11:42:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 23

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

\[ x +\frac {b y}{a +1}-y^{-a} c_1 = 0 \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 38

ode=(a*x+b*y[x])*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {\log \left (a+\frac {b y(x)}{x}+1\right )+a \log \left (\frac {y(x)}{x}\right )}{a+1}=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

RecursionError : maximum recursion depth exceeded