5.13 problem 24

Internal problem ID [4295]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number: 24.
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: 0.015 (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: 0.004 (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*}