28.1.123 problem 146

Internal problem ID [4429]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 146
Date solved : Tuesday, March 04, 2025 at 06:43:11 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.159 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.207 (sec). Leaf size: 24

ode=y[x]*Log[x]*Log[y[x]]+D[y[x],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: 0.307 (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)
 

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