13.3 problem 3

Internal problem ID [5597]

Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number: 3.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y=0} \end {gather*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 35

dsolve(diff(y(x),x$3)-y(x)=0,y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 49

DSolve[y'''[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^x+e^{-x/2} \left (c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_3 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \\ \end{align*}