10.1.25 problem 25

Internal problem ID [1122]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 25
Date solved : Monday, January 27, 2025 at 04:34:10 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (-\frac {\pi }{2}\right )&=a \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 19

dsolve([2*y(t)+t*diff(y(t),t) = sin(t)/t,y(-1/2*Pi) = a],y(t), singsol=all)
 

\[ y = \frac {-\cos \left (t \right )+\frac {a \,\pi ^{2}}{4}}{t^{2}} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 22

DSolve[{2*y[t]+t*D[y[t],t] == Sin[t]/t,y[-Pi/2]==a},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\pi ^2 a-4 \cos (t)}{4 t^2} \]