85.9.11 problem 1 (k)

Internal problem ID [22485]
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 37
Problem number : 1 (k)
Date solved : Thursday, October 02, 2025 at 08:40:58 PM
CAS classification : [_quadrature]

\begin{align*} i^{\prime }+5 i&=10 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 12

ode:=diff(i(t),t)+5*i(t) = 10; 
ic:=[i(0) = 0]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = 2-2 \,{\mathrm e}^{-5 t} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 14

ode=D[i[t],{t,1}]+5*i[t]==10; 
ic={i[0]==0}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to 2-2 e^{-5 t} \end{align*}

✓ Sympy. Time used: 0.071 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
i = Function("i") 
ode = Eq(5*i(t) + Derivative(i(t), t) - 10,0) 
ics = {i(0): 0} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = 2 - 2 e^{- 5 t} \]