73.15.64 problem 22.13 (b)

Internal problem ID [15495]
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 : 22.13 (b)
Date solved : Tuesday, January 28, 2025 at 07:59:43 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 59

dsolve(diff(y(x),x$5)+18*diff(y(x),x$3)+81*diff(y(x),x)=x^2*sin(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (18 x^{4}-7776 c_4 x -66 x^{2}-7776 c_{2} +2592 c_{3} +19\right ) \cos \left (3 x \right )}{23328}+\frac {\left (-12 x^{3}+\left (13+1944 c_{3} \right ) x +1944 c_{1} +648 c_4 \right ) \sin \left (3 x \right )}{5832}+c_5 \]

✓ Solution by Mathematica

Time used: 0.427 (sec). Leaf size: 198

DSolve[D[y[x],{x,5}]+18*D[y[x],{x,3}]+81*D[y[x],x]==x^2*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\left (c_1 \cos (3 K[5])+c_2 K[5] \cos (3 K[5])+\int _1^{K[5]}\frac {1}{54} K[1]^2 (3 \cos (3 K[1]) K[1]-\sin (3 K[1])) \sin (3 K[1])dK[1] \cos (3 K[5])+K[5] \int _1^{K[5]}-\frac {1}{36} K[2]^2 \sin (6 K[2])dK[2] \cos (3 K[5])+c_3 \sin (3 K[5])+c_4 K[5] \sin (3 K[5])+\sin (3 K[5]) \int _1^{K[5]}\frac {1}{54} K[3]^2 \sin (3 K[3]) (\cos (3 K[3])+3 K[3] \sin (3 K[3]))dK[3]+K[5] \sin (3 K[5]) \int _1^{K[5]}-\frac {1}{18} K[4]^2 \sin ^2(3 K[4])dK[4]\right )dK[5]+c_5 \]