29.5.6 problem 6

Internal problem ID [7275]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 04:27:41 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (4 x \right )+c_2 \cos \left (4 x \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 20

ode=D[y[x],{x,2}]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \cos (4 x)+c_2 \sin (4 x) \end{align*}

✓ Sympy. Time used: 0.026 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (4 x \right )} + C_{2} \cos {\left (4 x \right )} \]