73.17.13 problem 13

Internal problem ID [15476]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 13
Date solved : Monday, March 31, 2025 at 01:38:59 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-6*diff(diff(diff(diff(y(x),x),x),x),x)+13*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 60.112 (sec). Leaf size: 64

ode=D[y[x],{x,5}]-6*D[y[x],{x,4}]+13*D[y[x],{x,3}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^x\int _1^{K[3]}\int _1^{K[2]}e^{3 K[1]} (c_2 \cos (2 K[1])+c_1 \sin (2 K[1]))dK[1]dK[2]dK[3]+x (c_5 x+c_4)+c_3 \]

✓ Sympy. Time used: 0.097 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(13*Derivative(y(x), (x, 3)) - 6*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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