Internal problem ID [5598]
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: 4.
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: 0.002 (sec). Leaf size: 37
dsolve(diff(y(x),x$3)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 51
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_3 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \\ \end{align*}