15.10.23 problem 23

Internal problem ID [3110]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 23
Date solved : Tuesday, March 04, 2025 at 03:58:44 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

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

\[ y = {\mathrm e}^{x} c_{1} +c_2 \sin \left (\sqrt {2}\, x \right )+c_3 \cos \left (\sqrt {2}\, x \right )+c_4 \sin \left (2 x \right )+c_5 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 48

ode=D[y[x],{x,5}]-D[y[x],{x,4}]+6*D[y[x],{x,3}]-6*D[y[x],{x,2}]+8*D[y[x],x]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_5 e^x+c_1 \cos (2 x)+c_3 \cos \left (\sqrt {2} x\right )+c_2 \sin (2 x)+c_4 \sin \left (\sqrt {2} x\right ) \]

✓ Sympy. Time used: 0.220 (sec). Leaf size: 41

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

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