5.2.6 problem 13

Internal problem ID [1477]
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 : 13
Date solved : Tuesday, September 30, 2025 at 04:34:30 AM
CAS classification : [[_high_order, _missing_x]]

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

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

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

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

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 38

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

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

✓ Sympy. Time used: 0.049 (sec). Leaf size: 27

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

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