32.7.26 problem Exercise 20.27, page 220

Internal problem ID [5941]
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 20.27, page 220
Date solved : Tuesday, March 04, 2025 at 11:59:28 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

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

\[ y \left (x \right ) = \left (c_4 x +c_{2} \right ) \cos \left (\sqrt {2}\, x \right )+\sin \left (\sqrt {2}\, x \right ) \left (x c_3 +c_{1} \right ) \]

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

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

\[ y(x)\to (c_2 x+c_1) \cos \left (\sqrt {2} x\right )+(c_4 x+c_3) \sin \left (\sqrt {2} x\right ) \]

✓ Sympy. Time used: 0.089 (sec). Leaf size: 29

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

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