26.7.9 problem Exercise 20.10, page 220

Internal problem ID [7059]
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 20.10, 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 }-a^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 38

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 53

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

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

✓ Sympy. Time used: 0.081 (sec). Leaf size: 53

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

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