44.10.6 problem 1(f)

Internal problem ID [9261]
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 : 1(f)
Date solved : Tuesday, September 30, 2025 at 06:15:47 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 14*sin(2*x)-18*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} c_1 +{\mathrm e}^{x} c_2 +2 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==14*Sin[2*x]-18*Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 \sin (2 x)+3 \cos (2 x)+e^x \left (c_2 e^x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 14*sin(2*x) + 18*cos(2*x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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