54.4.31 problem 34

Internal problem ID [8615]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots Nonintegral. Exercises page 365
Problem number : 34
Date solved : Sunday, March 30, 2025 at 01:21:20 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=x^3*diff(diff(diff(y(x),x),x),x)+4*x^2*diff(diff(y(x),x),x)-8*x*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{6}+c_3 \,x^{5}+c_2}{x^{4}} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 22

ode=x^3*D[y[x],{x,3}]+4*x^2*D[y[x],{x,2}]-8*x*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1}{x^4}+c_3 x^2+c_2 x \]

✓ Sympy. Time used: 0.197 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 4*x**2*Derivative(y(x), (x, 2)) - 8*x*Derivative(y(x), x) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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