10.1.16 problem 16

Internal problem ID [1113]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 16
Date solved : Monday, January 27, 2025 at 04:33:52 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\pi \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

dsolve([2*y(t)/t+diff(y(t),t) = cos(t)/t^2,y(Pi) = 0],y(t), singsol=all)
 

\[ y = \frac {\sin \left (t \right )}{t^{2}} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 11

DSolve[{2*y[t]/t+D[y[t],t] == Cos[t]/t^2,y[Pi]==0},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\sin (t)}{t^2} \]