44.14.28 problem 4(d)

Internal problem ID [9352]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 4(d)
Date solved : Tuesday, September 30, 2025 at 06:16:49 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+y^{\prime }&=\frac {x -1}{x^{2}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+diff(y(x),x) = (x-1)/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left (-x \right )-{\mathrm e}^{-x} c_1 +c_2 \]

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 19

ode=D[y[x],{x,2}]+D[y[x],x]==(x-1)/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log (x)+c_1 \left (-e^{-x}\right )+c_2 \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + Derivative(y(x), (x, 2)) - (x - 1)/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + \log {\left (x \right )} \]