50.14.26 problem 4(b)

Internal problem ID [8064]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 4(b)
Date solved : Sunday, March 30, 2025 at 12:41:55 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=-8 \sin \left (3 x \right ) \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=\sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+y(x) = -8*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (x \right ) c_2 +\cos \left (x \right ) c_1 +\sin \left (3 x \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

ode=D[y[x],{x,2}]+y[x]==-8*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sin (3 x)+c_1 \cos (x)+c_2 \sin (x) \]

✓ Sympy. Time used: 0.064 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + 8*sin(3*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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