78.16.6 problem 6

Internal problem ID [18306]
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 23. Operator Methods for Finding Particular Solutions. Problems at page 169
Problem number : 6
Date solved : Thursday, March 13, 2025 at 11:53:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \,{\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-3*y(x) = 6*exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{-x} c_{1} +\frac {{\mathrm e}^{5 x}}{2} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]==6*Exp[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{5 x}}{2}+c_1 e^{-x}+c_2 e^{3 x} \]

✓ Sympy. Time used: 0.187 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x) - 6*exp(5*x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{3 x} + \frac {e^{5 x}}{2} \]