85.21.9 problem 2

Internal problem ID [22572]
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 : 2
Date solved : Thursday, October 02, 2025 at 08:51:53 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 11

ode:=diff(i(t),t)+2*i(t) = 10*exp(-2*t); 
ic:=[i(0) = 0]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = 10 \,{\mathrm e}^{-2 t} t \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 13

ode=D[i[t],t] +2*i[t]== 10*Exp[-2*t]; 
ic={i[0]==0}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to 10 e^{-2 t} t \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
i = Function("i") 
ode = Eq(2*i(t) + Derivative(i(t), t) - 10*exp(-2*t),0) 
ics = {i(0): 0} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = 10 t e^{- 2 t} \]