78.15.14 problem 14

Internal problem ID [18370]
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 : 14
Date solved : Tuesday, January 28, 2025 at 11:48:27 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(diff(y(x),x$4)+diff(y(x),x$3)-3*diff(y(x),x$2)-5*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_4 \,x^{2}+c_3 x +c_{2} \right ) {\mathrm e}^{-x}+c_{1} {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 32

DSolve[D[y[x],{x,4}]+D[y[x],{x,3}]-3*D[y[x],{x,2}]-5*D[y[x],x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (c_3 x^2+c_2 x+c_4 e^{3 x}+c_1\right ) \]