Internal problem ID [7697]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 117.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-x \,{\mathrm e}^{\frac {y}{x}}-y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 20
dsolve(x*diff(y(x),x) - x*exp(y(x)/x) - y(x) - x=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\ln \left (-\frac {x}{x \,{\mathrm e}^{c_{1}}-1}\right )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 3.741 (sec). Leaf size: 30
DSolve[x*y'[x] - x*Exp[y[x]/x] - y[x] - x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \log \left (-1+\frac {1}{1+e^{c_1} x}\right ) \\ y(x)\to i \pi x \\ \end{align*}