50.13.3 problem 3

Internal problem ID [8018]
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
Date solved : Monday, January 27, 2025 at 03:36:52 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 52

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

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