5.2.5 problem 12

Internal problem ID [1476]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.2, Higher order linear differential equations. Constant coefficients. page 180
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 04:34:29 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)-3*diff(diff(diff(diff(y(x),x),x),x),x)+3*diff(diff(y(x),x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (c_3 \,x^{2}+c_2 x +c_1 \right )+{\mathrm e}^{x} \left (c_6 \,x^{2}+c_5 x +c_4 \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 50

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

\begin{align*} y(x)&\to e^{-x} \left (x^2 \left (c_6 e^{2 x}+c_3\right )+x \left (c_5 e^{2 x}+c_2\right )+c_4 e^{2 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.063 (sec). Leaf size: 26

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

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