67.12.11 problem 19.2 (e)

Internal problem ID [16650]
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 : 19.2 (e)
Date solved : Thursday, October 02, 2025 at 01:37:22 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+2 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \end{align*}

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

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x)+4*diff(y(x),x)-8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 34

ode=D[y[x],{x,4}]+D[y[x],{x,3}]+2*D[y[x],{x,2}]+4*D[y[x],x]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.114 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) + 4*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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