49.9.5 problem 1(e)

Internal problem ID [7654]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 83
Problem number : 1(e)
Date solved : Wednesday, March 05, 2025 at 04:49:45 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(y(x),x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_{2} {\mathrm e}^{4 x}+c_4 \,{\mathrm e}^{3 x}+{\mathrm e}^{x} c_{1} +c_3 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 35

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

\[ y(x)\to e^{-2 x} \left (c_2 e^x+e^{3 x} \left (c_4 e^x+c_3\right )+c_1\right ) \]

✓ Sympy. Time used: 0.107 (sec). Leaf size: 26

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

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