62.22.3 problem Ex 3

Internal problem ID [12846]
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 : Wednesday, March 05, 2025 at 08:48:19 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.005 (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);
 

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

✓ Mathematica. Time used: 0.003 (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]
 

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

✓ Sympy. Time used: 0.180 (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)
 

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