Internal problem ID [6351]
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]]
\[ \boxed {y^{\prime \prime \prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$3)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{1} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 56
DSolve[y'''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (c_3 e^{3 x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{3 x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+c_1\right ) \]