85.21.5 problem 1 (e)

Internal problem ID [22568]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 55
Problem number : 1 (e)
Date solved : Thursday, October 02, 2025 at 08:51:47 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} i^{\prime }+3 i&={\mathrm e}^{-2 t} \end{align*}

With initial conditions

\begin{align*} i \left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 13

ode:=diff(i(t),t)+3*i(t) = exp(-2*t); 
ic:=[i(0) = 5]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = \left ({\mathrm e}^{t}+4\right ) {\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 16

ode=D[i[t],t] +3*i[t]==Exp[-2*t]; 
ic={i[0]==5}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to e^{-3 t} \left (e^t+4\right ) \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
i = Function("i") 
ode = Eq(3*i(t) + Derivative(i(t), t) - exp(-2*t),0) 
ics = {i(0): 5} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = \left (1 + 4 e^{- t}\right ) e^{- 2 t} \]