73.13.29 problem 20.4 (e)

Internal problem ID [15336]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.4 (e)
Date solved : Monday, March 31, 2025 at 01:34:42 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 x y^{\prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^3*diff(diff(diff(y(x),x),x),x)+15*x^2*diff(diff(y(x),x),x)+9*x*diff(y(x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 \ln \left (x \right )+c_2 \right ) \cos \left (2 \ln \left (x \right )\right )+\sin \left (2 \ln \left (x \right )\right ) \left (c_3 \ln \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 34

ode=x^4*D[y[x],{x,4}]+6*x^3*D[y[x],{x,3}]+15*x^2*D[y[x],{x,2}]+9*x*D[y[x],x]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (c_2 \log (x)+c_1) \cos (2 \log (x))+(c_4 \log (x)+c_3) \sin (2 \log (x)) \]

✓ Sympy. Time used: 0.378 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 6*x**3*Derivative(y(x), (x, 3)) + 15*x**2*Derivative(y(x), (x, 2)) + 9*x*Derivative(y(x), x) + 16*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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