Internal problem ID [976]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: Example 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y+x \,{\mathrm e}^{-\frac {y}{x}}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(y(x),x)=(y(x)+x*exp(-y(x)/x))/x,y(x), singsol=all)
\[ y \relax (x ) = \ln \left (\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.386 (sec). Leaf size: 13
DSolve[y'[x]==(y[x]+x*Exp[-y[x]/x])/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \log (\log (x)+c_1) \\ \end{align*}