23.3.504 problem 510

Internal problem ID [6218]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 510
Date solved : Tuesday, September 30, 2025 at 02:36:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

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

\[ y = c_1 \left (x -1\right )+c_2 \,{\mathrm e}^{x} x^{2} \]

✓ Mathematica. Time used: 0.139 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to c_1 e^x x^2+c_2 (x-1) \end{align*}

✗ Sympy

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

False