52.1.2 problem 3. direct method

Internal problem ID [8219]
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
Date solved : Monday, January 27, 2025 at 03:46:14 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

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

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

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