32.7.27 problem Exercise 20.28, page 220

Internal problem ID [5942]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.28, page 220
Date solved : Monday, January 27, 2025 at 01:27:52 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(diff(y(x),x$3)+8*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{3 x} \sin \left (\sqrt {3}\, x \right )+c_3 \,{\mathrm e}^{3 x} \cos \left (\sqrt {3}\, x \right )+c_{1} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 42

DSolve[D[y[x],{x,3}]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-2 x}+c_3 e^x \cos \left (\sqrt {3} x\right )+c_2 e^x \sin \left (\sqrt {3} x\right ) \]