78.15.4 problem 4

Internal problem ID [18360]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 22. Higher Order Linear Equations. Coupled Harmonic Oscillators. Problems at page 160
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 11:48:23 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 56

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

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