49.4.12 problem 3(c)

Internal problem ID [7623]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 52
Problem number : 3(c)
Date solved : Monday, January 27, 2025 at 03:07:54 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (\frac {\pi }{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 8

dsolve([diff(y(x),x$2)+y(x)=0,y(0) = 0, D(y)(1/2*Pi) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 10

DSolve[{D[y[x],{x,2}]+y[x]==0,{y[0]==0,Derivative[1][y][Pi/2]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \sin (x) \]