43.4.12 problem 3(c)

Internal problem ID [8909]
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 : Tuesday, September 30, 2025 at 06:00:00 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*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 8

ode:=diff(diff(y(x),x),x)+y(x) = 0; 
ic:=[y(0) = 0, D(y)(1/2*Pi) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = c_1 \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 10

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

\begin{align*} y(x)&\to c_1 \sin (x) \end{align*}

✓ Sympy. Time used: 0.029 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, pi/2): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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