12.18.12 problem section 9.2, problem 12

Internal problem ID [2126]
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 12
Date solved : Saturday, March 29, 2025 at 11:49:07 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+7 y^{\prime \prime }+5 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=6*diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(diff(y(x),x),x),x)+7*diff(diff(y(x),x),x)+5*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {x}{3}}+c_2 \,{\mathrm e}^{-\frac {x}{2}}+c_3 \sin \left (x \right )+c_4 \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 37

ode=6*D[y[x],{x,4}]+5*D[y[x],{x,3}]+7*D[y[x],{x,2}]+5*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x/2} \left (c_3 e^{x/6}+c_4\right )+c_1 \cos (x)+c_2 \sin (x) \]

✓ Sympy. Time used: 0.189 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + 5*Derivative(y(x), x) + 7*Derivative(y(x), (x, 2)) + 5*Derivative(y(x), (x, 3)) + 6*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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