67.11.33 problem 17.6 (c)

Internal problem ID [16634]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.6 (c)
Date solved : Thursday, October 02, 2025 at 01:37:14 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ y^{\prime }\left (0\right )&=12 \\ \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+16*y(x) = 0; 
ic:=[y(0) = 4, D(y)(0) = 12]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 3 \sin \left (4 x \right )+4 \cos \left (4 x \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

ode=D[y[x],{x,2}]+16*y[x]==0; 
ic={y[0]==4,Derivative[1][y][0] ==12}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 \sin (4 x)+4 \cos (4 x) \end{align*}

✓ Sympy. Time used: 0.036 (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 = {y(0): 4, Subs(Derivative(y(x), x), x, 0): 12} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 \sin {\left (4 x \right )} + 4 \cos {\left (4 x \right )} \]