Internal problem ID [13439]
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: 92
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)
\[ y = -\frac {11 x^{2} \cos \left (3 x \right )}{3888}+\frac {19 \cos \left (3 x \right )}{23328}+\frac {13 x \sin \left (3 x \right )}{5832}-\frac {\sin \left (3 x \right ) x^{3}}{486}+\frac {c_{1} \sin \left (3 x \right )}{3}-\frac {c_{2} \cos \left (3 x \right )}{3}+\frac {\cos \left (3 x \right ) x^{4}}{1296}+c_{3} \left (\frac {\cos \left (3 x \right )}{9}+\frac {x \sin \left (3 x \right )}{3}\right )+c_{4} \left (\frac {\sin \left (3 x \right )}{9}-\frac {x \cos \left (3 x \right )}{3}\right )+c_{5} \]
✓ Solution by Mathematica
Time used: 0.411 (sec). Leaf size: 72
DSolve[y'''''[x]+18*y'''[x]+81*y'[x]==x^2*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4 \left (-12 x^3+(13+1944 c_2) x+648 (3 c_1+c_4)\right ) \sin (3 x)+\left (18 x^4-66 x^2-7776 c_4 x+19+2592 c_2-7776 c_3\right ) \cos (3 x)}{23328}+c_5 \]