66.1.10 problem Problem 10

Internal problem ID [13857]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 10
Date solved : Tuesday, January 28, 2025 at 06:05:30 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.108 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.192 (sec). Leaf size: 38

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {\log (K[1])}{K[1] (\log (K[1])+1)}dK[1]=-\log (x)+c_1,y(x)\right ] \]