78.15.16 problem 19 (a)

Internal problem ID [18372]
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 : 19 (a)
Date solved : Tuesday, January 28, 2025 at 11:48:28 AM
CAS classification : [[_high_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$4)=0,y(x), singsol=all)
 

\[ y = \frac {1}{6} c_{1} x^{3}+\frac {1}{2} c_{2} x^{2}+c_3 x +c_4 \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 22

DSolve[D[y[x],{x,4}]==0,y[x],x,IncludeSingularSolutions -> True]
 

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