72.9.11 problem 5 (e)

Internal problem ID [19545]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 14. Introduction. Problems at page 112
Problem number : 5 (e)
Date solved : Thursday, October 02, 2025 at 04:39:59 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=6 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x) = 6*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-2 x} c_1}{2}+2 \,{\mathrm e}^{x}+c_2 \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 24

ode=D[y[x],{x,2}] +2* D[y[x],x]==6*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 e^x-\frac {1}{2} c_1 e^{-2 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*exp(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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