30.12.27 problem 26 (c)

Internal problem ID [7619]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 26 (c)
Date solved : Tuesday, September 30, 2025 at 04:55:02 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 )&=2 \\ y \left (\pi \right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 13

ode:=diff(diff(y(t),t),t)+y(t) = 0; 
ic:=[y(0) = 2, y(Pi) = -2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = c_1 \sin \left (t \right )+2 \cos \left (t \right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 15

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

\begin{align*} y(t)&\to 2 \cos (t)+c_2 \sin (t) \end{align*}

✓ Sympy. Time used: 0.035 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = C_{1} \sin {\left (t \right )} + 2 \cos {\left (t \right )} \]