52.5.1 problem 31

Internal problem ID [8324]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.2.2 TRANSFORMS OF DERIVATIVES Page 289
Problem number : 31
Date solved : Wednesday, March 05, 2025 at 05:35:12 AM
CAS classification : [_quadrature]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.658 (sec). Leaf size: 8

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 10

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

\[ y(t)\to e^t-1 \]

✓ Sympy. Time used: 0.124 (sec). Leaf size: 7

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

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