78.13.7 problem 1 (g)

Internal problem ID [18250]
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 (g)
Date solved : Thursday, March 13, 2025 at 11:50:54 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)+y(x) = 2*cos(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_{2} +x \right ) \sin \left (x \right )+\cos \left (x \right ) c_{1} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 20

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

\[ y(x)\to (1+c_1) \cos (x)+(x+c_2) \sin (x) \]

✓ Sympy. Time used: 0.069 (sec). Leaf size: 14

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

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