84.21.8 problem 13.8

Internal problem ID [22234]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 13. nth Order linear homogeneous differential equations with constant coefficients. Solved problems. Page 67
Problem number : 13.8
Date solved : Thursday, October 02, 2025 at 08:36:30 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-8*diff(diff(diff(y(x),x),x),x)+32*diff(diff(y(x),x),x)-64*diff(y(x),x)+64*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 36

ode=D[y[x],{x,4}]-8*D[y[x],{x,3}]+32*D[y[x],{x,2}]-64*D[y[x],{x,1}]+64*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.143 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(64*y(x) - 64*Derivative(y(x), x) + 32*Derivative(y(x), (x, 2)) - 8*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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