73.9.19 problem 14.2 (i)

Internal problem ID [15280]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.2 (i)
Date solved : Tuesday, January 28, 2025 at 07:51:30 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve([diff(y(x),x$2)+y(x)=0,sin(x)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 16

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

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