73.12.18 problem 19.4 (b)

Internal problem ID [15370]
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 : 19.4 (b)
Date solved : Tuesday, January 28, 2025 at 07:53:50 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+216 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

dsolve(diff(y(x),x$3)+216*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{9 x} \sin \left (3 \sqrt {3}\, x \right )+c_{3} {\mathrm e}^{9 x} \cos \left (3 \sqrt {3}\, x \right )+c_{1} \right ) {\mathrm e}^{-6 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 48

DSolve[D[y[x],{x,3}]+216*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-6 x} \left (c_3 e^{9 x} \cos \left (3 \sqrt {3} x\right )+c_2 e^{9 x} \sin \left (3 \sqrt {3} x\right )+c_1\right ) \]