67.12.23 problem 19.4 (g)

Internal problem ID [16662]
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 (g)
Date solved : Thursday, October 02, 2025 at 01:37:25 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 16 y^{\prime \prime \prime \prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 41

ode=16*D[y[x],{x,4}]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.049 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + 16*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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