56.3.28 problem 28

Internal problem ID [8886]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 28
Date solved : Monday, January 27, 2025 at 05:18:30 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {y}{x}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(diff(y(x),x)=exp(-y(x)/x),y(x), singsol=all)
 

\[ y = \operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}-\frac {1}{-{\mathrm e}^{-\textit {\_a}}+\textit {\_a}}d \textit {\_a} +\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.443 (sec). Leaf size: 39

DSolve[D[y[x],x]==Exp[-y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

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