65.13.8 problem 8

Internal problem ID [15815]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number : 8
Date solved : Thursday, October 02, 2025 at 10:28:16 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&={\mathrm e}^{x} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.090 (sec). Leaf size: 8

ode:=diff(y(x),x) = exp(x); 
ic:=[y(0) = -1]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

\[ y = {\mathrm e}^{x}-2 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 10

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

\begin{align*} y(x)&\to e^x-2 \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = e^{x} - 2 \]