13.2.18 problem 22

Internal problem ID [2316]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 22
Date solved : Saturday, March 29, 2025 at 11:53:54 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(y(t),t)+1/t*y(t) = cos(t)+sin(t)/t; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 14

ode=D[y[t],t]+1/t*y[t]==Cos[t]+Sin[t]/t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \sin (t)+\frac {c_1}{t} \]

✓ Sympy. Time used: 0.299 (sec). Leaf size: 8

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

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