44.10.7 problem 1(g)

Internal problem ID [9262]
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(g)
Date solved : Tuesday, September 30, 2025 at 06:15:47 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (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: 0.015 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to \sin (x) \int _1^x2 \cos ^2(K[1])dK[1]+\cos ^3(x)+c_1 \cos (x)+c_2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.039 (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)
 

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