67.15.16 problem 22.7 (a)

Internal problem ID [16734]
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 : 22.7 (a)
Date solved : Thursday, October 02, 2025 at 01:38:18 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

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

\[ y = \sin \left (3 x \right ) c_2 +\cos \left (3 x \right ) c_1 +5 x \cos \left (2 x \right )+4 \sin \left (2 x \right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to 4 \sin (2 x)+5 x \cos (2 x)+c_1 \cos (3 x)+c_2 \sin (3 x) \end{align*}

✓ Sympy. Time used: 0.055 (sec). Leaf size: 31

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

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