85.37.5 problem 1 (e)

Internal problem ID [22748]
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 175
Problem number : 1 (e)
Date solved : Thursday, October 02, 2025 at 09:14:18 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} i^{\prime \prime }-4 i^{\prime }+2 i&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=diff(diff(i(t),t),t)-4*diff(i(t),t)+2*i(t) = 0; 
dsolve(ode,i(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 34

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

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

✓ Sympy. Time used: 0.125 (sec). Leaf size: 26

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

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