60.1.339 problem 346

Internal problem ID [10353]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 346
Date solved : Sunday, March 30, 2025 at 04:23:05 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.045 (sec). Leaf size: 19

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

\[ \left (x y\right )^{-a x +y}-c_1 = 0 \]

✓ Mathematica. Time used: 0.327 (sec). Leaf size: 24

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

\[ \text {Solve}[a x \log (x y(x))-y(x) \log (x y(x))=c_1,y(x)] \]

✗ Sympy

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

Timed Out