78.13.5 problem 1 (e)

Internal problem ID [18248]
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 18. The Method of Undetermined Coefficients. Problems at page 132
Problem number : 1 (e)
Date solved : Thursday, March 13, 2025 at 11:50:51 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-6*y(x) = 20*exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_{2} {\mathrm e}^{5 x}+c_{1} -4 x \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 32

ode=D[y[x],{x,2}] -D[y[x],x]-6*y[x]==20*Exp[-2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{5} e^{-2 x} \left (-20 x+5 c_2 e^{5 x}-4+5 c_1\right ) \]

✓ Sympy. Time used: 0.224 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 20*exp(-2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{3 x} + \left (C_{1} - 4 x\right ) e^{- 2 x} \]