78.23.1 problem 3 (a)

Internal problem ID [18373]
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 : Thursday, March 13, 2025 at 11:55:10 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*}

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

ode:=diff(y(x),x)+y(x) = 3*exp(2*x); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.136 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 3*exp(2*x) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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