32.7.28 problem Exercise 20.29, page 220

Internal problem ID [5943]
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 20.29, page 220
Date solved : Tuesday, March 04, 2025 at 11:59:29 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.152 (sec). Leaf size: 32

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

\[ y(x)\to c_4 x-\frac {1}{4} c_1 \cos (2 x)-\frac {1}{4} c_2 \sin (2 x)+c_3 \]

✓ Sympy. Time used: 0.055 (sec). Leaf size: 20

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

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