78.23.1 problem 3 (a)

Internal problem ID [18452]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 9. Laplace transforms. Section 50. Applications to differential equations. Problems at page 462
Problem number : 3 (a)
Date solved : Tuesday, January 28, 2025 at 11:50:18 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=3 \,{\mathrm e}^{2 x} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.228 (sec). Leaf size: 15

dsolve([diff(y(x),x)+y(x)=3*exp(2*x),y(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 18

DSolve[{D[y[x],x]+y[x]==3*Exp[2*x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{3 x}-1\right ) \]