71.13.9 problem 9

Internal problem ID [14529]
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 : 9
Date solved : Tuesday, January 28, 2025 at 06:43:00 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=2 \,{\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: 8.781 (sec). Leaf size: 12

dsolve([diff(y(x),x)-y(x)=2*exp(x),y(0) = 1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (2 x +1\right ) \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 14

DSolve[{D[y[x],x]-y[x]==2*Exp[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (2 x+1) \]