83.3.8 problem 3

Internal problem ID [21927]
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. IV at page 38
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:13:16 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.163 (sec). Leaf size: 46

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

\[ y = x \left ({\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}}-x^{-\frac {2 a}{b +a}} {\mathrm e}^{-\frac {2 c_1 a +\textit {\_Z} a -\textit {\_Z} b}{b +a}}+2\right )}+1\right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 48

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

\[ \text {Solve}\left [\frac {1}{2} (a-b) \log \left (1-\frac {y(x)}{x}\right )+\frac {1}{2} (a+b) \log \left (\frac {y(x)}{x}+1\right )=-a \log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

RecursionError : maximum recursion depth exceeded