78.13.6 problem 1 (f)

Internal problem ID [18257]
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 (f)
Date solved : Monday, March 31, 2025 at 05:24:01 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: 0.016 (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]
 

\[ y(x)\to 2 \sin (2 x)+3 \cos (2 x)+e^x \left (c_2 e^x+c_1\right ) \]

✓ Sympy. Time used: 0.225 (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)
 

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