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 : Monday, January 27, 2025 at 09:17:01 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[y[x]*Log[x]*Log[y[x]]+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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