65.9.8 problem 8

Internal problem ID [15774]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 8
Date solved : Thursday, October 02, 2025 at 10:27:48 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (x \right )+c_2 \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to c_1 \cos (x)+c_2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.020 (sec). Leaf size: 12

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

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