43.22.12 problem 2(d)

Internal problem ID [9044]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 198
Problem number : 2(d)
Date solved : Tuesday, September 30, 2025 at 06:02:23 PM
CAS classification : [_quadrature]

\begin{align*} {\mathrm e}^{y}+x \,{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=exp(y(x))+x*exp(y(x))+x*exp(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x -\ln \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 16

ode=(Exp[y[x]]+x*Exp[y[x]])+(x*Exp[y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -x-\log (x)-1+c_1 \end{align*}

✓ Sympy. Time used: 0.134 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = C_{1} - x - \log {\left (x \right )} \]