Internal problem ID [5203]
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(d).
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*} With initial conditions \begin {align*} \left [y \relax (0) = 0, y \left (\frac {\pi }{2}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 5
dsolve([diff(y(x),x$2)+y(x)=0,y(0) = 0, y(1/2*Pi) = 0],y(x), singsol=all)
\[ y \relax (x ) = 0 \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 6
DSolve[{y''[x]+y[x]==0,{y[0]==0,y[Pi/2]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ \end{align*}