9.9.27 problem 41

Internal problem ID [3084]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 41
Date solved : Tuesday, September 30, 2025 at 06:26:56 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x)-13*diff(diff(diff(y(x),x),x),x)-13*diff(diff(y(x),x),x)+36*diff(y(x),x)+36*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_5 \,{\mathrm e}^{6 x}+c_1 \,{\mathrm e}^{5 x}+c_2 \,{\mathrm e}^{2 x}+c_4 \,{\mathrm e}^{x}+c_3 \right ) {\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 42

ode=D[y[x],{x,5}]+D[y[x],{x,4}]-13*D[y[x],{x,3}]-13*D[y[x],{x,2}]+36*D[y[x],x]+36*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} \left (e^x \left (c_3 e^x+e^{4 x} \left (c_5 e^x+c_4\right )+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) + 36*Derivative(y(x), x) - 13*Derivative(y(x), (x, 2)) - 13*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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