10.6.8 problem 8

Internal problem ID [1225]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 8
Date solved : Saturday, March 29, 2025 at 10:48:13 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 16

ode:=2*y(x)+x*diff(y(x),x) = sin(x)/x; 
ic:=y(2) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {-\cos \left (x \right )+4+\cos \left (2\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 17

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

\[ y(x)\to \frac {-\cos (x)+4+\cos (2)}{x^2} \]

✓ Sympy. Time used: 0.361 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {- \cos {\left (x \right )} + \cos {\left (2 \right )} + 4}{x^{2}} \]