30.11.4 problem 4

Internal problem ID [7584]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.1 at page 156
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 04:54:37 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+18 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 15

ode:=2*diff(diff(y(t),t),t)+18*y(t) = 0; 
ic:=[y(0) = 2, D(y)(0) = 3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \sin \left (3 t \right )+2 \cos \left (3 t \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 16

ode=2*D[y[t],{t,2}]+0*D[y[t],t]+18*y[t]==0; 
ic={y[0]==2,Derivative[1][y][0] ==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \sin (3 t)+2 \cos (3 t) \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(18*y(t) + 2*Derivative(y(t), (t, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \sin {\left (3 t \right )} + 2 \cos {\left (3 t \right )} \]