74.12.1 problem 1

Internal problem ID [16237]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 1
Date solved : Monday, March 31, 2025 at 02:48:00 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(diff(y(t),t),t)+4*y(t) = 1; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \sin \left (2 t \right ) c_2 +\cos \left (2 t \right ) c_1 +\frac {1}{4} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 23

ode=D[y[t],{t,2}]+4*y[t]==1; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to c_1 \cos (2 t)+c_2 \sin (2 t)+\frac {1}{4} \]

✓ Sympy. Time used: 0.066 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) + Derivative(y(t), (t, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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