26.6.25 problem Exercise 12.25, page 103

Internal problem ID [7025]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.25, page 103
Date solved : Tuesday, September 30, 2025 at 04:16:19 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x y^{\prime }-y \left (\ln \left (x y\right )-1\right )&=0 \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 14

ode:=x*diff(y(x),x)-y(x)*(ln(x*y(x))-1) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\frac {x}{c_1}}}{x} \]

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 24

ode=x*D[y[x],x]-y[x]*(Log[x*y[x]]-1)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{e^{c_1} x}}{x}\\ y(x)&\to \frac {1}{x} \end{align*}

✓ Sympy. Time used: 0.245 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - (log(x*y(x)) - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{C_{1} x}}{x} \]