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 : Monday, January 27, 2025 at 04:45:57 AM
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*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

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

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

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