29.8.12 problem 217

Internal problem ID [4817]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 217
Date solved : Sunday, March 30, 2025 at 03:59:52 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.278 (sec). Leaf size: 26

ode=x D[y[x],x]+(1-Log[x]-Log[y[x]])y[x]==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: 0.676 (sec). Leaf size: 8

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

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