Internal problem ID [13622]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients.
Additional exercises page 369
Problem number: 19.1 (f).
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$5)+18*diff(y(x),x$3)+81*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{5} x +c_{3} \right ) \cos \left (3 x \right )+\left (c_{4} x +c_{2} \right ) \sin \left (3 x \right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 48
DSolve[y'''''[x]+18*y'''[x]+81*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{9} ((c_2-3 (c_4 x+c_3)) \cos (3 x)+(3 c_2 x+3 c_1+c_4) \sin (3 x)+9 c_5) \]