68.5.55 problem 62

Internal problem ID [17306]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 62
Date solved : Thursday, October 02, 2025 at 02:01:19 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 25

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

\begin{align*} y(t)&\to \frac {\int _1^t\cos (K[1]) K[1]dK[1]+c_1}{t} \end{align*}

✓ Sympy. Time used: 0.183 (sec). Leaf size: 14

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

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