73.15.26 problem 22.9 (d)

Internal problem ID [15386]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.9 (d)
Date solved : Monday, March 31, 2025 at 01:36:13 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=3 \sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)+9*y(x) = 3*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 c_1 -x \right ) \cos \left (3 x \right )}{2}+\sin \left (3 x \right ) c_2 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 62

ode=D[y[x],{x,2}]+9*y[x]==3*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sin (3 x) \int _1^x\frac {1}{2} \sin (6 K[2])dK[2]+\cos (3 x) \int _1^x-\sin ^2(3 K[1])dK[1]+c_1 \cos (3 x)+c_2 \sin (3 x) \]

✓ Sympy. Time used: 0.124 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 3*sin(3*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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