23.3.333 problem 335

Internal problem ID [6047]
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 : 335
Date solved : Tuesday, September 30, 2025 at 02:20:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

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

\[ y = \frac {\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right ) c_2 -2 \,{\mathrm e}^{-\frac {x^{2}}{2}} c_2 x +c_1}{x} \]

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 49

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

\begin{align*} y(x)&\to \frac {\sqrt {2 \pi } c_2 \text {erf}\left (\frac {x}{\sqrt {2}}\right )-2 c_2 e^{-\frac {x^2}{2}} x+2 c_1}{2 x} \end{align*}

✗ Sympy

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

False