88.4.4 problem 4

Internal problem ID [23968]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 33
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:48:02 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 15

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

\[ y = c_1 \,{\mathrm e}^{\left (x +1\right ) {\mathrm e}^{-x}} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 24

ode=x*y[x]+Exp[x]*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{e^{-x} (x+1)}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.210 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} e^{\left (x + 1\right ) e^{- x}} \]