73.12.26 problem 19.4 (j)

Internal problem ID [15307]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.4 (j)
Date solved : Monday, March 31, 2025 at 01:33:48 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+16 y^{\prime \prime \prime }+64 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 43

ode:=diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)+16*diff(diff(diff(y(x),x),x),x)+64*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_6 x +c_4 \right ) \cos \left (\sqrt {3}\, x \right )+{\mathrm e}^{x} \left (c_5 x +c_3 \right ) \sin \left (\sqrt {3}\, x \right )+{\mathrm e}^{-2 x} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 60

ode=D[y[x],{x,6}]+16*D[y[x],{x,3}]+64*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (c_6 x+e^{3 x} (c_4 x+c_3) \cos \left (\sqrt {3} x\right )+e^{3 x} (c_2 x+c_1) \sin \left (\sqrt {3} x\right )+c_5\right ) \]

✓ Sympy. Time used: 0.194 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(64*y(x) + 16*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 6)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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