Internal problem ID [13759]
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).
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }=x^{2} \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {\left (18 x^{4}-7776 c_{4} x -66 x^{2}-7776 c_{2} +2592 c_{3} +19\right ) \cos \left (3 x \right )}{23328}+\frac {\left (-12 x^{3}+\left (13+1944 c_{3} \right ) x +1944 c_{1} +648 c_{4} \right ) \sin \left (3 x \right )}{5832}+c_{5} \]
✓ Solution by Mathematica
Time used: 0.411 (sec). Leaf size: 72
DSolve[y'''''[x]+18*y'''[x]+81*y'[x]==x^2*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4 \left (-12 x^3+(13+1944 c_2) x+648 (3 c_1+c_4)\right ) \sin (3 x)+\left (18 x^4-66 x^2-7776 c_4 x+19+2592 c_2-7776 c_3\right ) \cos (3 x)}{23328}+c_5 \]