73.6.8 problem 7.4 (f)

Internal problem ID [15076]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.4 (f)
Date solved : Monday, March 31, 2025 at 01:22:37 PM
CAS classification : [[_homogeneous, `class G`], _exact]

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

✓ Maple. Time used: 0.078 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.183 (sec). Leaf size: 17

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

\[ y(x)\to \frac {e^{\frac {c_1}{x}}}{x} \]

✓ Sympy. Time used: 0.476 (sec). Leaf size: 8

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

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