12.2.13 problem 13

Internal problem ID [1549]
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 : 13
Date solved : Saturday, March 29, 2025 at 10:58:35 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = \frac {{\mathrm e}^{x} c_1 +2}{x} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 17

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

\[ y(x)\to \frac {2+c_1 e^x}{x} \]

✓ Sympy. Time used: 0.238 (sec). Leaf size: 10

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

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