42.2.6 problem Example 3.23

Internal problem ID [8808]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.3 SECOND ORDER ODE. Page 147
Problem number : Example 3.23
Date solved : Tuesday, September 30, 2025 at 05:52:43 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=4 \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+y(x) = 4*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 -2 x \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_2 +2\right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 41

ode=D[y[x],{x,2}]+y[x]==4*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \cos (x) \int _1^x-4 \sin ^2(K[1])dK[1]-2 \sin (x) \cos ^2(x)+c_1 \cos (x)+c_2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 4*sin(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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