81.10.18 problem 14-18

Internal problem ID [21613]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 14. Second order homogeneous differential equations with constant coefficients. Page 297.
Problem number : 14-18
Date solved : Thursday, October 02, 2025 at 07:59:02 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 )&=0 \\ y^{\prime }\left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 10

ode:=diff(diff(y(x),x),x)+16*y(x) = 0; 
ic:=[y(0) = 0, D(y)(0) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {5 \sin \left (4 x \right )}{4} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 13

ode=D[y[x],{x,2}]+16*y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] ==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {5}{4} \sin (4 x) \end{align*}

✓ Sympy. Time used: 0.035 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {5 \sin {\left (4 x \right )}}{4} \]