71.10.8 problem 8

Internal problem ID [14432]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 8
Date solved : Monday, March 31, 2025 at 12:27:02 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-3*diff(diff(diff(diff(y(x),x),x),x),x)+3*diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 43

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

\[ y(x)\to \int _1^x\left (e^{K[1]} \left (c_3+e^{K[1]} c_4\right )+c_1 \cos (K[1])+c_2 \sin (K[1])\right )dK[1]+c_5 \]

✓ Sympy. Time used: 0.202 (sec). Leaf size: 26

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

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