85.67.5 problem 5

Internal problem ID [22896]
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 216
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:16:23 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} i^{\prime \prime }+2 i^{\prime }+5 i&=34 \cos \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(diff(i(t),t),t)+2*diff(i(t),t)+5*i(t) = 34*cos(2*t); 
dsolve(ode,i(t), singsol=all);
 

\[ i = \left (c_1 \cos \left (2 t \right )+c_2 \sin \left (2 t \right )\right ) {\mathrm e}^{-t}+2 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 38

ode=D[i[t],{t,2}]+2*D[i[t],t]+5*i[t]==34*Cos[2*t]; 
ic={}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to e^{-t} \left (\left (2 e^t+c_2\right ) \cos (2 t)+\left (8 e^t+c_1\right ) \sin (2 t)\right ) \end{align*}

✓ Sympy. Time used: 0.155 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
i = Function("i") 
ode = Eq(5*i(t) - 34*cos(2*t) + 2*Derivative(i(t), t) + Derivative(i(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = \left (C_{1} \sin {\left (2 t \right )} + C_{2} \cos {\left (2 t \right )}\right ) e^{- t} + 8 \sin {\left (2 t \right )} + 2 \cos {\left (2 t \right )} \]