Internal problem ID [5454]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page
28
Problem number: 1(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-y-2 x \,{\mathrm e}^{-\frac {y}{x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x*diff(y(x),x)=y(x)+2*x*exp(-y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \ln \left (2 \ln \relax (x )+2 c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.619 (sec). Leaf size: 15
DSolve[x*y'[x]==y[x]+2*x*Exp[-y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \log (2 \log (x)+c_1) \\ \end{align*}