78.1.32 problem 2 (r)

Internal problem ID [18087]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (r)
Date solved : Tuesday, January 28, 2025 at 11:25:55 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

Time used: 0.162 (sec). Leaf size: 18

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

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