74.12.1 problem 1

Internal problem ID [16308]
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 : Tuesday, January 28, 2025 at 09:02:32 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(diff(y(t),t$2)+4*y(t)=1,y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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