23.3.480 problem 486

Internal problem ID [6194]
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 : 486
Date solved : Tuesday, September 30, 2025 at 02:36:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to c_1 e^{\frac {1}{x}} \operatorname {ExpIntegralEi}\left (-\frac {1}{x}\right )+c_1 x+c_2 e^{\frac {1}{x}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - 2*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, 2)) + 2*y(x))/