71.13.8 problem 8

Internal problem ID [14528]
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 : Tuesday, January 28, 2025 at 06:43:00 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*}

Solution by Maple

Time used: 9.053 (sec). Leaf size: 8

dsolve([diff(y(x),x)=exp(x),y(0) = -1],y(x), singsol=all)
 
\[ y = {\mathrm e}^{x}-2 \]

Solution by Mathematica

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

DSolve[{D[y[x],x]==Exp[x],{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to e^x-2 \]