85.40.4 problem 1 (d)

Internal problem ID [22761]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 177
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 09:14:25 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-4 y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

ode:=diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)-4*diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 x +c_3 \,x^{2}+c_4 \,x^{3}+c_5 \,{\mathrm e}^{-2 x}+c_6 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 44

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

\begin{align*} y(x)&\to c_6 x^3+c_5 x^2+c_4 x+\frac {1}{16} e^{-2 x} \left (c_1 e^{4 x}+c_2\right )+c_3 \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 31

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

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