Internal problem ID [13438]
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]]
\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }=x^{2} {\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 74
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)
\[ y = -\frac {x \,{\mathrm e}^{3 x}}{486}+\frac {5 \,{\mathrm e}^{3 x}}{4374}+\frac {x^{2} {\mathrm e}^{3 x}}{972}+\frac {c_{1} \sin \left (3 x \right )}{3}-\frac {c_{2} \cos \left (3 x \right )}{3}+c_{3} \left (\frac {\cos \left (3 x \right )}{9}+\frac {x \sin \left (3 x \right )}{3}\right )+c_{4} \left (\frac {\sin \left (3 x \right )}{9}-\frac {x \cos \left (3 x \right )}{3}\right )+c_{5} \]
✓ 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]
\[ y(x)\to \frac {e^{3 x} \left (9 x^2-18 x+10\right )}{8748}+\frac {1}{9} (c_2-3 (c_4 x+c_3)) \cos (3 x)+\frac {1}{9} (3 c_2 x+3 c_1+c_4) \sin (3 x)+c_5 \]