73.12.6 problem 19.1 (f)

Internal problem ID [15358]
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)
Date solved : Tuesday, January 28, 2025 at 07:53:45 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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)
 

\[ y = \left (x c_5 +c_{3} \right ) \cos \left (3 x \right )+\left (c_4 x +c_{2} \right ) \sin \left (3 x \right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 44

DSolve[D[y[x],{x,5}]+18*D[y[x],{x,3}]+81*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x(\cos (3 K[1]) (c_1+c_2 K[1])+(c_3+c_4 K[1]) \sin (3 K[1]))dK[1]+c_5 \]