20.1.2 problem Problem 8

Internal problem ID [3559]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 8
Date solved : Monday, January 27, 2025 at 07:43:58 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

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

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