50.13.15 problem 15

Internal problem ID [8030]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 15
Date solved : Monday, January 27, 2025 at 03:36:57 PM
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: 0.003 (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)
 

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

✓ Solution by Mathematica

Time used: 0.004 (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]
 

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