90.8.2 problem 2

Internal problem ID [25176]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 2. The Laplace Transform. Exercises at page 109
Problem number : 2
Date solved : Thursday, October 02, 2025 at 11:57:35 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-4 y&=1 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.037 (sec). Leaf size: 12

ode:=diff(y(t),t)-4*y(t) = 1; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = -\frac {1}{4}+\frac {{\mathrm e}^{4 t}}{4} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 16

ode=D[y[t],t]-4*y[t]==1; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{4} \left (e^{4 t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*y(t) + Derivative(y(t), t) - 1,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {e^{4 t}}{4} - \frac {1}{4} \]