73.15.71 problem 22.14 (b)

Internal problem ID [15431]
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 : 22.14 (b)
Date solved : Monday, March 31, 2025 at 01:37:24 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 42

ode:=diff(diff(y(x),x),x)+9*y(x) = 25*x*cos(2*x)+3*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x +2 c_1 \right ) \cos \left (3 x \right )}{2}+\frac {\left (1+12 c_2 \right ) \sin \left (3 x \right )}{12}+5 x \cos \left (2 x \right )+4 \sin \left (2 x \right ) \]

✓ Mathematica. Time used: 0.638 (sec). Leaf size: 96

ode=D[y[x],{x,2}]+9*y[x]==25*x*Cos[2*x]+3*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \cos (3 x) \int _1^x-\frac {1}{3} \sin (3 K[1]) (25 \cos (2 K[1]) K[1]+3 \sin (3 K[1]))dK[1]+\sin (3 x) \int _1^x\frac {1}{3} \cos (3 K[2]) (25 \cos (2 K[2]) K[2]+3 \sin (3 K[2]))dK[2]+c_1 \cos (3 x)+c_2 \sin (3 x) \]

✓ Sympy. Time used: 0.166 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-25*x*cos(2*x) + 9*y(x) - 3*sin(3*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} \sin {\left (3 x \right )} + 5 x \cos {\left (2 x \right )} + \left (C_{1} - \frac {x}{2}\right ) \cos {\left (3 x \right )} + 4 \sin {\left (2 x \right )} \]