87.3.1 problem 1

Internal problem ID [23250]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 26
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:27:00 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+\left (1+x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=(1+x)*y(x)+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,{\mathrm e}^{-x}}{x} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.177 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + (x + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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