74.8.23 problem 23

Internal problem ID [16088]
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 : Monday, March 31, 2025 at 02:41:26 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ r = \frac {\cos \left (t \right )+t \sin \left (t \right )+c_1}{t} \]

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

ode=t*D[r[t],t]+r[t]==t*Cos[t]; 
ic={}; 
DSolve[{ode,ic},r[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.287 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
r = Function("r") 
ode = Eq(-t*cos(t) + t*Derivative(r(t), t) + r(t),0) 
ics = {} 
dsolve(ode,func=r(t),ics=ics)
 

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