89.13.10 problem 10

Internal problem ID [24593]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 127
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:46:22 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 )&=y_{0} \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 8

ode:=diff(diff(y(x),x),x)+y(x) = 0; 
ic:=[y(0) = y__0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = y_{0} \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 9

ode=D[y[x],{x,2}]+y[x] ==0; 
ic={y[0]==y0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {y0} \cos (x) \end{align*}

✓ Sympy. Time used: 0.028 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y0 = symbols("y0") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): y0, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = y_{0} \cos {\left (x \right )} \]