50.3.28 problem 28

Internal problem ID [10172]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 28
Date solved : Tuesday, September 30, 2025 at 07:10:59 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

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

\[ y = \operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}-\frac {1}{-{\mathrm e}^{-\textit {\_a}}+\textit {\_a}}d \textit {\_a} +\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.269 (sec). Leaf size: 39

ode=D[y[x],x]==Exp[-y[x]/x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.685 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - exp(-y(x)/x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \int \limits ^{\frac {x}{y{\left (x \right )}}} \frac {1}{u_{1} - e^{\frac {1}{u_{1}}}}\, du_{1}} \]