Internal problem ID [13760]
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 (c).
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }=\sin \left (3 x \right ) {\mathrm e}^{3 x} x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 73
dsolve(diff(y(x),x$5)+18*diff(y(x),x$3)+81*diff(y(x),x)=x^2*exp(3*x)*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-75 x^{2}-310 x +417\right ) {\mathrm e}^{3 x}-303750 c_{4} x -303750 c_{2} +101250 c_{3} \right ) \cos \left (3 x \right )}{911250}+\frac {\left (-1575 x^{2}+3240 x -1693\right ) \sin \left (3 x \right ) {\mathrm e}^{3 x}}{2733750}+\frac {\left (3 c_{3} x +3 c_{1} +c_{4} \right ) \sin \left (3 x \right )}{9}+c_{5} \]
✓ Solution by Mathematica
Time used: 0.792 (sec). Leaf size: 94
DSolve[y'''''[x]+18*y'''[x]+81*y'[x]==x^2*Exp[3*x]*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {e^{3 x} \left (1575 x^2-3240 x+1693\right ) \sin (3 x)}{2733750}-\frac {e^{3 x} \left (75 x^2+310 x-417\right ) \cos (3 x)}{911250}+\frac {1}{9} (c_2-3 (c_4 x+c_3)) \cos (3 x)+\frac {1}{9} (3 c_2 x+3 c_1+c_4) \sin (3 x)+c_5 \]