Internal problem ID [6465]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{-\frac {y}{x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(x),x)=exp(-y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{{\mathrm e}^{-\textit {\_a}}-\textit {\_a}}d \textit {\_a} \right )+\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.259 (sec). Leaf size: 39
DSolve[y'[x]==Exp[-y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {e^{K[1]}}{e^{K[1]} K[1]-1}dK[1]=-\log (x)+c_1,y(x)\right ] \]