Internal problem ID [2575]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 7, page 37
Problem number: 1..
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D]]
Solve \begin {gather*} \boxed {y^{\prime } x -y-2 \,{\mathrm e}^{-\frac {y}{x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x)=y(x)+2*exp(- y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \ln \left (\frac {2 x c_{1}-2}{x}\right ) x \]
✓ Solution by Mathematica
Time used: 0.575 (sec). Leaf size: 16
DSolve[x*y'[x]==y[x]+2*Exp[- y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \log \left (-\frac {2}{x}+c_1\right ) \\ \end{align*}