56.22.3 problem Ex 3

Internal problem ID [14206]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 44. Roots of auxiliary equation repeated. Page 94
Problem number : Ex 3
Date solved : Thursday, October 02, 2025 at 09:26:43 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} -y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)-2*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to e^{-x} \left (c_3 x^2+c_2 x+c_4 e^{2 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 19

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

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