Internal problem ID [5017]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-y \ln \left (\frac {y}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)=y(x)*ln(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{c_{1} x +1} x \]
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 24
DSolve[x*y'[x]==y[x]*Log[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x e^{1+e^{c_1} x} \\ y(x)\to e x \\ \end{align*}