73.13.30 problem 20.4 (f)

Internal problem ID [15337]
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 (f)
Date solved : Monday, March 31, 2025 at 01:34:43 PM
CAS classification : [[_high_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

\[ y = \frac {c_1 \,x^{6}+c_4 \,x^{4}+c_2 \,x^{2}+c_3}{x^{3}} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 28

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

\[ y(x)\to c_4 x^3+\frac {c_1}{x^3}+c_3 x+\frac {c_2}{x} \]

✓ Sympy. Time used: 0.245 (sec). Leaf size: 19

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)) - 3*x**2*Derivative(y(x), (x, 2)) - 9*x*Derivative(y(x), x) + 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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