10.1.18 problem 18

Internal problem ID [1115]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 18
Date solved : Monday, January 27, 2025 at 04:33:56 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 22

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

\[ y = \frac {\sin \left (t \right )-\cos \left (t \right ) t +\frac {\pi ^{2}}{4}-1}{t^{2}} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 26

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

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