44.14.9 problem 2(a)

Internal problem ID [9333]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 2(a)
Date solved : Tuesday, September 30, 2025 at 06:16:30 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)+9*y(x) = 0; 
ic:=[y(0) = 1, D(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

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

ode=D[y[x],{x,2}]+9*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.036 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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