64.10.19 problem 19

Internal problem ID [13354]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 19
Date solved : Monday, March 31, 2025 at 07:52:13 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

\[ y = \left (c_5 x +c_4 \right ) {\mathrm e}^{x}+c_3 \,x^{2}+c_2 x +c_1 \]

✓ Mathematica. Time used: 0.079 (sec). Leaf size: 30

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

\[ y(x)\to e^x (c_2 (x-3)+c_1)+x (c_5 x+c_4)+c_3 \]

✓ Sympy. Time used: 0.080 (sec). Leaf size: 22

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

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