Internal problem ID [7218]
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]
\[ \boxed {y^{\prime }-{\mathrm e}^{-\frac {y}{x}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(x),x)=exp(-y(x)/x),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (-\left (\int _{}^{\textit {\_Z}}-\frac {1}{-{\mathrm e}^{-\textit {\_a}}+\textit {\_a}}d \textit {\_a} \right )+\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 39
DSolve[y'[x]==Exp[-y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {e^{K[1]}}{e^{K[1]} K[1]-1}dK[1]=-\log (x)+c_1,y(x)\right ] \]