85.40.3 problem 1 (c)

Internal problem ID [22760]
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 177
Problem number : 1 (c)
Date solved : Thursday, October 02, 2025 at 09:14:24 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 i^{\prime \prime }-12 i^{\prime }+9 i&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=4*diff(diff(i(t),t),t)-12*diff(i(t),t)+9*i(t) = 0; 
dsolve(ode,i(t), singsol=all);
 

\[ i = {\mathrm e}^{\frac {3 t}{2}} \left (c_2 t +c_1 \right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 34

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

\begin{align*} i(t)&\to e^{-3 \left (\sqrt {3}-2\right ) t} \left (c_2 e^{6 \sqrt {3} t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 29

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

\[ i{\left (t \right )} = C_{1} e^{3 t \left (2 - \sqrt {3}\right )} + C_{2} e^{3 t \left (\sqrt {3} + 2\right )} \]