29.8.10 problem 215

Internal problem ID [4815]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 215
Date solved : Monday, January 27, 2025 at 09:41:05 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 18

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

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