23.1.131 problem 135

Internal problem ID [4738]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 135
Date solved : Tuesday, September 30, 2025 at 08:20:45 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.104 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.126 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.173 (sec). Leaf size: 14

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

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