29.20.16 problem 561

Internal problem ID [5157]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 561
Date solved : Tuesday, March 04, 2025 at 08:19:57 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.181 (sec). Leaf size: 60

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

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

✓ Mathematica. Time used: 0.171 (sec). Leaf size: 36

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

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

✗ Sympy

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

RecursionError : maximum recursion depth exceeded