78.15.15 problem 15

Internal problem ID [18371]
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 : 15
Date solved : Tuesday, January 28, 2025 at 11:48:28 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 31

dsolve(diff(y(x),x$5)-6*diff(y(x),x$4)-8*diff(y(x),x$3)+48*diff(y(x),x$2)+16*diff(y(x),x)-96*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_5 x +c_4 \right ) {\mathrm e}^{-2 x}+\left (c_3 x +c_{2} \right ) {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{6 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 43

DSolve[D[y[x],{x,5}]-6*D[y[x],{x,4}]-8*D[y[x],{x,3}]+48*D[y[x],{x,2}]+16*D[y[x],x]-96*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_2 x+c_3 e^{4 x}+c_4 e^{4 x} x+c_5 e^{8 x}+c_1\right ) \]