43.4.10 problem 3(a)

Internal problem ID [8907]
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 : Tuesday, September 30, 2025 at 05:59:57 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*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to 2 \sin (x)+\cos (x) \end{align*}

✓ Sympy. Time used: 0.027 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, y(pi/2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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