16.1.9 problem 3(c)

Internal problem ID [3411]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(c)
Date solved : Tuesday, March 04, 2025 at 04:37:56 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

\[ y \left (x \right ) = \ln \left (2\right )+\ln \left (\frac {1}{x^{2}+2 c_{1}}\right ) \]

✓ Mathematica. Time used: 0.297 (sec). Leaf size: 19

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

\[ y(x)\to \log (2)-\log \left (x^2-2 c_1\right ) \]

✓ Sympy. Time used: 0.177 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \log {\left (\frac {1}{C_{1} + x^{2}} \right )} + \log {\left (2 \right )} \]