85.42.7 problem 2 (a)

Internal problem ID [22776]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 180
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 09:14:33 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 )&=4 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 8

ode:=diff(diff(y(x),x),x)+y(x) = 0; 
ic:=[y(0) = 4, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 4 \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 9

ode=D[y[x],{x,2}]+y[x]==0; 
ic={y[0]==4,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4 \cos (x) \end{align*}

✓ Sympy. Time used: 0.042 (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): 4, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 4 \cos {\left (x \right )} \]