74.5.47 problem 54

Internal problem ID [15940]
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 : 54
Date solved : Monday, March 31, 2025 at 02:14:02 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y&=8 \cos \left (4 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(t),t)+4*y(t) = 8*cos(4*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \sin \left (4 t \right )+\cos \left (4 t \right )+{\mathrm e}^{-4 t} c_1 \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 34

ode=D[y[t],t]+4*y[t]==8*Cos[4*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-4 t} \left (\int _1^t8 e^{4 K[1]} \cos (4 K[1])dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) - 8*cos(4*t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 4 t} + \sin {\left (4 t \right )} + \cos {\left (4 t \right )} \]