74.8.23 problem 23

Internal problem ID [16159]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 08:53:07 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

dsolve(t*diff(r(t),t)+r(t)=t*cos(t),r(t), singsol=all)
 

\[ r = \frac {t \sin \left (t \right )+\cos \left (t \right )+c_{1}}{t} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 25

DSolve[t*D[r[t],t]+r[t]==t*Cos[t],r[t],t,IncludeSingularSolutions -> True]
 

\[ r(t)\to \frac {\int _1^t\cos (K[1]) K[1]dK[1]+c_1}{t} \]