1.2 problem 3. direct method

Internal problem ID [5798]

Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. Section 6.2 SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number: 3. direct method.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+y=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 13

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

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

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 16

DSolve[y''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}