71.10.9 problem 9

Internal problem ID [14433]
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 : 9
Date solved : Monday, March 31, 2025 at 12:27:03 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 40

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(diff(y(x),x),x),x)+35*diff(diff(y(x),x),x)+16*diff(y(x),x)-52*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 \sin \left (3 x \right ) {\mathrm e}^{4 x}+c_5 \cos \left (3 x \right ) {\mathrm e}^{4 x}+c_1 \,{\mathrm e}^{3 x}+c_3 x +c_2 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 50

ode=D[y[x],{x,5}]-D[y[x],{x,4}]+D[y[x],{x,3}]+35*D[y[x],{x,2}]+16*D[y[x],x]-52*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (c_4 x+c_5 e^{3 x}+c_2 e^{4 x} \cos (3 x)+c_1 e^{4 x} \sin (3 x)+c_3\right ) \]

✓ Sympy. Time used: 0.296 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-52*y(x) + 16*Derivative(y(x), x) + 35*Derivative(y(x), (x, 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)
 

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