76.2.16 problem 16

Internal problem ID [17352]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 10:02:07 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {2 y}{t}&=\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: 0.012 (sec). Leaf size: 10

dsolve([diff(y(t),t)+(2/t)*y(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: 0.035 (sec). Leaf size: 19

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

\[ y(t)\to \frac {\int _{\pi }^t\cos (K[1])dK[1]}{t^2} \]