23.5.123 problem 123

Internal problem ID [6732]
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 : 123
Date solved : Friday, October 03, 2025 at 02:09:50 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -4 \left (3 x^{2}+1\right ) y+2 x \left (5 x^{2}+2\right ) y^{\prime }-2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.078 (sec). Leaf size: 23

ode:=-4*(3*x^2+1)*y(x)+2*x*(5*x^2+2)*diff(y(x),x)-2*x^2*(2*x^2+1)*diff(diff(y(x),x),x)+x^3*(x^2+1)*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.196 (sec). Leaf size: 46

ode=-4*(1 + 3*x^2)*y[x] + 2*x*(2 + 5*x^2)*D[y[x],x] - 2*x^2*(1 + 2*x^2)*D[y[x],{x,2}] + x^3*(1 + x^2)*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} x \left (c_2 x^2-2 c_1 \left (x^2-3 x+1\right )-2 c_2 x+c_3 x+c_3 x \log (x)+c_2\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*(x**2 + 1)*Derivative(y(x), (x, 3)) - 2*x**2*(2*x**2 + 1)*Derivative(y(x), (x, 2)) + 2*x*(5*x**2 + 2)*Derivative(y(x), x) + (-12*x**2 - 4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**5*Derivative(y(x), (x, 3)) + 4*x**4*D