87.13.26 problem 30

Internal problem ID [23509]
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 : 30
Date solved : Thursday, October 02, 2025 at 09:42:34 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{5} y^{\left (5\right )}+3 x^{3} y^{\prime \prime \prime }-9 x^{2} y^{\prime \prime }+18 x y^{\prime }-18 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=x^5*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+3*x^3*diff(diff(diff(y(x),x),x),x)-9*x^2*diff(diff(y(x),x),x)+18*x*diff(y(x),x)-18*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\left (c_5 \,x^{2}+c_3 \right ) \ln \left (x \right )+c_4 \,x^{2}+c_1 x +c_2 \right ) x \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 31

ode=x^5*D[y[x],{x,5}]+3*x^3*D[y[x],{x,3}]-9*x^2*D[y[x],{x,2}]+18*x*D[y[x],x]-18*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \left (\left (c_5 x^2+c_2\right ) \log (x)+x (c_4 x+c_3)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**5*Derivative(y(x), (x, 5)) + 3*x**3*Derivative(y(x), (x, 3)) - 9*x**2*Derivative(y(x), (x, 2)) + 18*x*Derivative(y(x), x) - 18*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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