23.3.8 problem 7(h)

Internal problem ID [4149]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 7(h)
Date solved : Sunday, March 30, 2025 at 02:41:02 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \end{align*}

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

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(diff(y(x),x),x),x)-9*diff(diff(y(x),x),x)-11*diff(y(x),x)-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{5 x}+c_4 \,x^{2}+c_3 x +c_2 \right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 32

ode=D[y[x],{x,4}]-D[y[x],{x,3}]-9*D[y[x],{x,2}]-11*D[y[x],x]-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} \left (c_3 x^2+c_2 x+c_4 e^{5 x}+c_1\right ) \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) - 11*Derivative(y(x), x) - 9*Derivative(y(x), (x, 2)) - Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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