26.7.8 problem Exercise 20.9, page 220

Internal problem ID [7058]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.9, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:02 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

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

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 49

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

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

✓ Sympy. Time used: 0.172 (sec). Leaf size: 37

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

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