23.5.88 problem 88

Internal problem ID [6697]
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 : 88
Date solved : Friday, October 03, 2025 at 02:09:46 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.163 (sec). Leaf size: 41

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

\begin{align*} y(x)&\to \frac {1}{4} \left (2 c_1 x^2+2 i c_2 e^{-i x}-c_3 e^{i x}\right ) \end{align*}

✗ Sympy

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

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