23.5.110 problem 110

Internal problem ID [6719]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 110
Date solved : Tuesday, September 30, 2025 at 03:51:07 PM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=6*y(x)+18*x*diff(y(x),x)+9*x^2*diff(diff(y(x),x),x)+(x^3+1)*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{2}+c_2 x +c_3}{\left (x +1\right ) \left (x^{2}-x +1\right )} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 31

ode=6*y[x] + 18*x*D[y[x],x] + 9*x^2*D[y[x],{x,2}] + (1 + x^3)*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_3 x^2+2 c_2 x+2 c_1}{2 x^3+2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2*Derivative(y(x), (x, 2)) + 18*x*Derivative(y(x), x) + (x**3 + 1)*Derivative(y(x), (x, 3)) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x**2*(-x*Derivative(y(x), (x, 3)) - 9*Der