Internal problem ID [13440]
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]]
\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 118
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)
\[ y = c_{5} -\frac {31 x \,{\mathrm e}^{3 x} \cos \left (3 x \right )}{91125}+\frac {4 x \,{\mathrm e}^{3 x} \sin \left (3 x \right )}{3375}+\frac {139 \,{\mathrm e}^{3 x} \cos \left (3 x \right )}{303750}-\frac {1693 \,{\mathrm e}^{3 x} \sin \left (3 x \right )}{2733750}+\frac {c_{3} x \sin \left (3 x \right )}{3}-\frac {c_{4} x \cos \left (3 x \right )}{3}-\frac {x^{2} {\mathrm e}^{3 x} \cos \left (3 x \right )}{12150}-\frac {7 x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right )}{12150}+\frac {c_{1} \sin \left (3 x \right )}{3}-\frac {c_{2} \cos \left (3 x \right )}{3}+\frac {\cos \left (3 x \right ) c_{3}}{9}+\frac {c_{4} \sin \left (3 x \right )}{9} \]
✓ 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]
\[ y(x)\to -\frac {e^{3 x} \left (1575 x^2-3240 x+1693\right ) \sin (3 x)}{2733750}-\frac {e^{3 x} \left (75 x^2+310 x-417\right ) \cos (3 x)}{911250}+\frac {1}{9} (c_2-3 (c_4 x+c_3)) \cos (3 x)+\frac {1}{9} (3 c_2 x+3 c_1+c_4) \sin (3 x)+c_5 \]