49.4.10 problem 3(a)

Internal problem ID [7621]
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)
Date solved : Monday, January 27, 2025 at 03:07:49 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 )&=1\\ y \left (\frac {\pi }{2}\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.009 (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)
 

\[ y = \cos \left (x \right )+2 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 12

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

\[ y(x)\to 2 \sin (x)+\cos (x) \]