85.33.45 problem 45

Internal problem ID [22668]
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 65
Problem number : 45
Date solved : Thursday, October 02, 2025 at 09:03:28 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(i(t),t)+i(t) = exp(t); 
dsolve(ode,i(t), singsol=all);
 

\[ i = \frac {{\mathrm e}^{t}}{2}+{\mathrm e}^{-t} c_1 \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 21

ode=D[i[t],{t,1}]+i[t]==Exp[t]; 
ic={}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to \frac {e^t}{2}+c_1 e^{-t} \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 12

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

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