85.42.9 problem 2 (c)

Internal problem ID [22778]
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 (c)
Date solved : Thursday, October 02, 2025 at 09:14:35 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} i^{\prime \prime }+2 i^{\prime }+5 i&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 20

ode:=diff(diff(i(t),t),t)+2*diff(i(t),t)+5*i(t) = 0; 
ic:=[i(0) = 2, D(i)(0) = 0]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = {\mathrm e}^{-t} \left (\sin \left (2 t \right )+2 \cos \left (2 t \right )\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 22

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

\begin{align*} i(t)&\to e^{-t} (\sin (2 t)+2 \cos (2 t)) \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 17

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

\[ i{\left (t \right )} = \left (\sin {\left (2 t \right )} + 2 \cos {\left (2 t \right )}\right ) e^{- t} \]