73.12.4 problem 19.1 (d)

Internal problem ID [15356]
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 (d)
Date solved : Tuesday, January 28, 2025 at 07:53:45 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-81 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(x),x$4)-81*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 36

DSolve[D[y[x],{x,4}]-81*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{3 x}+c_3 e^{-3 x}+c_2 \cos (3 x)+c_4 \sin (3 x) \]