78.15.9 problem 9

Internal problem ID [18365]
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 : 9
Date solved : Tuesday, January 28, 2025 at 11:48:25 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(x),x$4)+2*a^2*diff(y(x),x$2)+a^4*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_4 x +c_{2} \right ) \cos \left (a x \right )+\sin \left (a x \right ) \left (c_3 x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[D[y[x],{x,4}]+2*a^2*D[y[x],{x,2}]+a^4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 x+c_1) \cos (a x)+(c_4 x+c_3) \sin (a x) \]