87.13.14 problem 14

Internal problem ID [23497]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 100
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:42:27 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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);
 

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

✓ Mathematica. Time used: 0.004 (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]
 

\begin{align*} y(x)&\to \frac {c_1}{x^4}+c_3 x^2+c_2 x \end{align*}

✓ Sympy. Time used: 0.127 (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)
 

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