44.10.14 problem 4(a)

Internal problem ID [9269]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED COEFFICIENTS. Page 67
Problem number : 4(a)
Date solved : Tuesday, September 30, 2025 at 06:15:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

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

\[ y = {\mathrm e}^{\sqrt {3}\, x} c_2 +{\mathrm e}^{-\sqrt {3}\, x} c_1 +{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to e^{2 x}+c_1 e^{\sqrt {3} x}+c_2 e^{-\sqrt {3} x} \end{align*}

✓ Sympy. Time used: 0.052 (sec). Leaf size: 27

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

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