77.1.68 problem 88 (page 123)

Internal problem ID [17958]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 88 (page 123)
Date solved : Tuesday, January 28, 2025 at 11:18:20 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.119 (sec). Leaf size: 9

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

\[ y = {\mathrm e}^{{\mathrm e}^{x} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.160 (sec). Leaf size: 18

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

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