Internal problem ID [5200]
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(a).
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) = 1, y \left (\frac {\pi }{2}\right ) = 2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve([diff(y(x),x$2)+y(x)=0,y(0) = 1, y(1/2*Pi) = 2],y(x), singsol=all)
\[ y \relax (x ) = \cos \relax (x )+2 \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 12
DSolve[{y''[x]+y[x]==0,{y[0]==1,y[Pi/2]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \sin (x)+\cos (x) \\ \end{align*}