38.6.34 problem 34

Internal problem ID [8464]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 34
Date solved : Tuesday, September 30, 2025 at 05:37:33 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 15

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

\[ y = \frac {\ln \left (x \right )+{\mathrm e}}{x +1} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 15

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

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

✓ Sympy. Time used: 0.134 (sec). Leaf size: 12

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

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