73.15.14 problem 22.5 (d)

Internal problem ID [15445]
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 : Tuesday, January 28, 2025 at 07:55:59 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+9*y(x)=9*x^4-9,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 33

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

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