Internal problem ID [2729]
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: 115.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y+{\mathrm e}^{\frac {y}{x}} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)= y(x)-x*exp(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = -\ln \left (c_{1}+\ln \relax (x )\right ) x \]
✓ Solution by Mathematica
Time used: 0.443 (sec). Leaf size: 16
DSolve[x*y'[x]== y[x]-x*Exp[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \log (\log (x)-c_1) \\ \end{align*}