38.3.15 problem 23

Internal problem ID [8282]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 23
Date solved : Tuesday, September 30, 2025 at 05:21:36 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

\[ y = \left (c_1 +x +1\right ) \cos \left (x \right )+\sin \left (x \right ) \left (x +c_2 \right ) \]

✓ Mathematica. Time used: 0.213 (sec). Leaf size: 64

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

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

✓ Sympy. Time used: 0.046 (sec). Leaf size: 15

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

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