23.5.113 problem 113

Internal problem ID [6722]
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 : 113
Date solved : Tuesday, September 30, 2025 at 03:51:09 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \frac {c_1 \,{\mathrm e}^{x}}{x}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.079 (sec). Leaf size: 21

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

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

✗ Sympy

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

NotImplementedError : CRootOf is not supported over ZZ[x]