Internal problem ID [13758]
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).
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }={\mathrm e}^{3 x} x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {\left (-3 c_{4} x -3 c_{2} +c_{3} \right ) \cos \left (3 x \right )}{9}+\frac {\left (9 x^{2}-18 x +10\right ) {\mathrm e}^{3 x}}{8748}+\frac {\left (3 c_{3} x +3 c_{1} +c_{4} \right ) \sin \left (3 x \right )}{9}+c_{5} \]
✓ Solution by Mathematica
Time used: 0.497 (sec). Leaf size: 67
DSolve[y'''''[x]+18*y'''[x]+81*y'[x]==x^2*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{3 x} \left (9 x^2-18 x+10\right )}{8748}+\frac {1}{9} (c_2-3 (c_4 x+c_3)) \cos (3 x)+\frac {1}{9} (3 c_2 x+3 c_1+c_4) \sin (3 x)+c_5 \]