76.2.33 problem 41

Internal problem ID [17298]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 41
Date solved : Monday, March 31, 2025 at 03:49:55 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

ode:=diff(y(t),t)+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: 0.053 (sec). Leaf size: 28

ode=D[y[t],t]+1/t*y[t]==3*Cos[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {\int _1^t3 \cos (2 K[1]) K[1]dK[1]+c_1}{t} \]

✓ Sympy. Time used: 0.322 (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)
 

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