73.15.63 problem 22.13 (a)

Internal problem ID [15494]
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 (a)
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} {\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 52

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

\[ y = \frac {\left (-3 c_4 x -3 c_{2} +c_{3} \right ) \cos \left (3 x \right )}{9}+\frac {\left (9 x^{2}-18 x +10\right ) {\mathrm e}^{3 x}}{8748}+\frac {\left (3 x c_{3} +c_4 +3 c_{1} \right ) \sin \left (3 x \right )}{9}+c_5 \]

✓ Solution by Mathematica

Time used: 0.366 (sec). Leaf size: 62

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

\[ y(x)\to \int _1^x\left (\frac {e^{3 K[1]} (2-3 K[1])^2}{2916}+\cos (3 K[1]) (c_1+c_2 K[1])+(c_3+c_4 K[1]) \sin (3 K[1])\right )dK[1]+c_5 \]