3.28 problem 28

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]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {e^{K[1]}}{e^{K[1]} K[1]-1}dK[1]=-\log (x)+c_1,y(x)\right ] \]