73.15.15 problem 22.6

Internal problem ID [15446]
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 : 22.6
Date solved : Tuesday, January 28, 2025 at 07:56:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=x^{3} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)+9*y(x)=x^3,y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {2 \sin \left (3 x \right )}{81}+\frac {x^{3}}{9}-\frac {2 x}{27} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

DSolve[{D[y[x],{x,2}]+9*y[x]==x^3,{y[0]==0,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{81} \left (9 x^3-6 x+2 \sin (3 x)\right ) \]