85.42.8 problem 2 (b)

Internal problem ID [22777]
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 (b)
Date solved : Thursday, October 02, 2025 at 09:14:34 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 8

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

\[ u = \sin \left (4 x \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 9

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

\begin{align*} u(x)&\to \sin (4 x) \end{align*}

✓ Sympy. Time used: 0.046 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
u = Function("u") 
ode = Eq(16*u(x) + Derivative(u(x), (x, 2)),0) 
ics = {u(0): 0, Subs(Derivative(u(x), x), x, 0): 4} 
dsolve(ode,func=u(x),ics=ics)
 

\[ u{\left (x \right )} = \sin {\left (4 x \right )} \]