76.12.11 problem 22

Internal problem ID [17567]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 10:44:10 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(t),t$2)+4*y(t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[D[y[t],{t,2}]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 \cos (2 t)+c_2 \sin (2 t) \]