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 : Wednesday, March 05, 2025 at 05:23:30 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*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-6*diff(diff(diff(diff(y(x),x),x),x),x)-8*diff(diff(diff(y(x),x),x),x)+48*diff(diff(y(x),x),x)+16*diff(y(x),x)-96*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 43

ode=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; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.259 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-96*y(x) + 16*Derivative(y(x), x) + 48*Derivative(y(x), (x, 2)) - 8*Derivative(y(x), (x, 3)) - 6*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{5} e^{6 x} + \left (C_{1} + C_{2} x\right ) e^{- 2 x} + \left (C_{3} + C_{4} x\right ) e^{2 x} \]