23.3.532 problem 538

Internal problem ID [6246]
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 : 538
Date solved : Tuesday, September 30, 2025 at 02:38:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1+2 x \right ) y-2 x^{2} y^{\prime }+x^{4} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=(2*x+1)*y(x)-2*x^2*diff(y(x),x)+x^4*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 20

ode=(1 + 2*x)*y[x] - 2*x^2*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^{-1/x} (c_2 x+c_1) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 2)) - 2*x**2*Derivative(y(x), x) + (2*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)) + 2*x*y(x)