82.4.8 problem 28-8

Internal problem ID [21826]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 28. Laplace transforms. Page 850
Problem number : 28-8
Date solved : Thursday, October 02, 2025 at 08:02:37 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+b y&=1 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 17

ode:=diff(y(t),t)+b*y(t) = 1; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \frac {1-{\mathrm e}^{-b t}}{b} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to \frac {1-e^{-b t}}{b} \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
b = symbols("b") 
y = Function("y") 
ode = Eq(b*y(t) + Derivative(y(t), t) - 1,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {1}{b} - \frac {e^{- b t}}{b} \]