23.5.107 problem 107

Internal problem ID [6716]
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 : 107
Date solved : Friday, October 03, 2025 at 02:09:48 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 18

ode:=-2*(x^2+4)*y(x)+x*(x^2+8)*diff(y(x),x)-4*x^2*diff(diff(y(x),x),x)+x^3*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left (\cos \left (x \right ) c_2 +\sin \left (x \right ) c_3 +c_1 x \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 23

ode=-2*(4 + x^2)*y[x] + x*(8 + x^2)*D[y[x],x] - 4*x^2*D[y[x],{x,2}] + x^3*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x (c_1 x+c_3 \cos (x)-c_2 \sin (x)) \end{align*}

✗ Sympy

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)) + x*(x**2 + 8)*Derivative(y(x), x) + (-2*x**2 - 8)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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