85.53.7 problem 2 (a)

Internal problem ID [22820]
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 197
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 09:14:57 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} i^{\prime \prime }+9 i&=12 \cos \left (3 t \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 18

ode:=diff(diff(i(t),t),t)+9*i(t) = 12*cos(3*t); 
ic:=[i(0) = 4, D(i)(0) = 0]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = 4 \cos \left (3 t \right )+2 \sin \left (3 t \right ) t \]

✓ Mathematica. Time used: 0.067 (sec). Leaf size: 19

ode=D[i[t],{t,2}]+9*i[t]==12*Cos[3*t]; 
ic={i[0]==4,Derivative[1][i][0] ==0}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to 2 t \sin (3 t)+4 \cos (3 t) \end{align*}

✓ Sympy. Time used: 0.071 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
i = Function("i") 
ode = Eq(9*i(t) - 12*cos(3*t) + Derivative(i(t), (t, 2)),0) 
ics = {i(0): 4, Subs(Derivative(i(t), t), t, 0): 0} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = 2 t \sin {\left (3 t \right )} + 4 \cos {\left (3 t \right )} \]