78.15.12 problem 12

Internal problem ID [18368]
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 : 12
Date solved : Tuesday, January 28, 2025 at 11:48:26 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

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

\[ y = \left (\left (c_{2} x +c_{1} \right ) {\mathrm e}^{3 x}+c_3 \sin \left (x \right )+c_4 \cos \left (x \right )\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 35

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

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