12.18.8 problem section 9.2, problem 8

Internal problem ID [2122]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 8
Date solved : Saturday, March 29, 2025 at 11:49:03 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = c_1 +c_2 x +c_3 \sin \left (x \right )+c_4 \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 24

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

\[ y(x)\to c_4 x-c_1 \cos (x)-c_2 \sin (x)+c_3 \]

✓ Sympy. Time used: 0.061 (sec). Leaf size: 17

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

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