4.1.4 problem 4

Internal problem ID [1101]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 04:21:48 AM
CAS classification : [_linear]

\begin{align*} \frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=y(t)/t+diff(y(t),t) = 3*cos(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {4 c_1 +6 \sin \left (2 t \right ) t +3 \cos \left (2 t \right )}{4 t} \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 30

ode=y[t]/t+D[y[t],t] == 3*Cos[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {6 t \sin (2 t)+3 \cos (2 t)+4 c_1}{4 t} \end{align*}

✓ Sympy. Time used: 0.206 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*cos(2*t) + Derivative(y(t), t) + y(t)/t,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{t} + \frac {3 \sin {\left (2 t \right )}}{2} + \frac {3 \cos {\left (2 t \right )}}{4 t} \]