23.3.534 problem 540

Internal problem ID [6248]
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 : 540
Date solved : Tuesday, September 30, 2025 at 02:38:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -\left (1+x \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=-(1+x)*y(x)+x^3*diff(y(x),x)+x^4*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 24

ode=-((1 + x)*y[x]) + x^3*D[y[x],x] + x^4*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{\frac {1}{x}} \left (c_1-c_2 \operatorname {ExpIntegralEi}\left (-\frac {2}{x}\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 2)) + x**3*Derivative(y(x), x) + (-x - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**4*Derivative(y(x), (x, 2)) + x*y(x) +