6.2.6 problem 6

Internal problem ID [1542]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 04:35:44 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 14

ode:=diff(y(x),x)+(1+x)/x*y(x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{1-x}}{x} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.145 (sec). Leaf size: 10

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

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