83.11.5 problem 5

Internal problem ID [21994]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter VI. Linear equations with constant coefficients. Ex. XIII at page 106
Problem number : 5
Date solved : Thursday, October 02, 2025 at 08:21:31 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-6*diff(diff(diff(y(x),x),x),x)+7*diff(diff(y(x),x),x)+6*diff(y(x),x)-8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{4 x}+c_3 \,{\mathrm e}^{-x}+c_4 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 36

ode=D[y[x],{x,4}]-6*D[y[x],{x,3}]+7*D[y[x],{x,2}]+6*D[y[x],x]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-x}+c_2 e^x+c_3 e^{2 x}+c_4 e^{4 x} \end{align*}

✓ Sympy. Time used: 0.285 (sec). Leaf size: 114

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) - 8*Derivative(y(x), x) + 7*Derivative(y(x), (x, 2)) - 6*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (3 - \sqrt {2}\right )}{2}} \sin {\left (\frac {x \sqrt {-11 + 14 \sqrt {2}}}{2} \right )} + C_{2} e^{\frac {x \left (3 - \sqrt {2}\right )}{2}} \cos {\left (\frac {x \sqrt {-11 + 14 \sqrt {2}}}{2} \right )} + C_{3} e^{\frac {x \left (\sqrt {2} + 3 + \sqrt {11 + 14 \sqrt {2}}\right )}{2}} + C_{4} e^{\frac {x \left (- \sqrt {11 + 14 \sqrt {2}} + \sqrt {2} + 3\right )}{2}} \]