23.5.89 problem 89

Internal problem ID [6698]
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 : 89
Date solved : Friday, October 03, 2025 at 02:09:46 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 17

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

\[ y = c_1 x +c_2 \,x^{2}+c_3 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 27

ode=-2*y[x] + 2*x*D[y[x],x] - x^2*D[y[x],{x,2}] + (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 {1}{2} \left (c_2 x^2+2 c_1 x+c_3 e^x\right ) \end{align*}

✗ Sympy

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

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