Internal problem ID [2647]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y \left (1+\ln \relax (y)-\ln \relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)=y(x)*(1+ln(y(x))-ln(x)),y(x), singsol=all)
\[ y \relax (x ) = x \,{\mathrm e}^{-c_{1} x} \]
✓ Solution by Mathematica
Time used: 0.213 (sec). Leaf size: 20
DSolve[x*y'[x]==y[x]*(1+Log[y[x]]-Log[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x e^{e^{c_1} x} \\ y(x)\to x \\ \end{align*}