26.7.18 problem Exercise 20.19, page 220

Internal problem ID [7068]
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 20.19, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:06 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 42

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

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

✓ Sympy. Time used: 0.043 (sec). Leaf size: 27

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

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