12.18.33 problem section 9.2, problem 43(g)

Internal problem ID [2147]
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 43(g)
Date solved : Saturday, March 29, 2025 at 11:49:28 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 53

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

\[ y = \left ({\mathrm e}^{\frac {x}{2}} c_5 +c_3 \,{\mathrm e}^{-\frac {x}{2}}\right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\left ({\mathrm e}^{\frac {x}{2}} c_4 +c_2 \,{\mathrm e}^{-\frac {x}{2}}\right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_1 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 70

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

\[ y(x)\to e^{-x} \left (e^{x/2} \left (c_3 e^x+c_2\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+e^{x/2} \left (c_4 e^x+c_1\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )+c_5\right ) \]

✓ Sympy. Time used: 0.290 (sec). Leaf size: 65

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

\[ y{\left (x \right )} = C_{5} e^{- x} + \left (C_{1} \sin {\left (\frac {\sqrt {3} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {3} x}{2} \right )}\right ) e^{- \frac {x}{2}} + \left (C_{3} \sin {\left (\frac {\sqrt {3} x}{2} \right )} + C_{4} \cos {\left (\frac {\sqrt {3} x}{2} \right )}\right ) e^{\frac {x}{2}} \]