67.15.14 problem 22.5 (d)

Internal problem ID [16732]
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 : 22.5 (d)
Date solved : Thursday, October 02, 2025 at 01:38:17 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=9 x^{4}-9 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)+9*y(x) = 9*x^4-9; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (3 x \right ) c_2 +\cos \left (3 x \right ) c_1 +x^{4}-\frac {4 x^{2}}{3}-\frac {19}{27} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 33

ode=D[y[x],{x,2}]+9*y[x]==9*x^4-9; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^4-\frac {4 x^2}{3}+c_1 \cos (3 x)+c_2 \sin (3 x)-\frac {19}{27} \end{align*}

✓ Sympy. Time used: 0.054 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*x**4 + 9*y(x) + Derivative(y(x), (x, 2)) + 9,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (3 x \right )} + C_{2} \cos {\left (3 x \right )} + x^{4} - \frac {4 x^{2}}{3} - \frac {19}{27} \]