78.11.1 problem 2 (a)

Internal problem ID [18272]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 16. The Use of a Known Solution to find Another. Problems at page 121
Problem number : 2 (a)
Date solved : Tuesday, January 28, 2025 at 11:44:59 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)
 

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 16

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

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