84.21.7 problem 13.7

Internal problem ID [22233]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 13. nth Order linear homogeneous differential equations with constant coefficients. Solved problems. Page 67
Problem number : 13.7
Date solved : Thursday, October 02, 2025 at 08:36:29 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 46

ode=D[y[x],{x,5}]-D[y[x],{x,4}]-2*D[y[x],{x,3}]+2*D[y[x],{x,2}]+D[y[x],{x,1}]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} \left (c_5 e^{2 x} x^2+x \left (c_4 e^{2 x}+c_2\right )+c_3 e^{2 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 22

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

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