23.3.128 problem 130

Internal problem ID [5842]
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 : 130
Date solved : Tuesday, September 30, 2025 at 02:04:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -4 x y+x^{2} y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 31

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

\[ y = c_1 x \left (x^{3}+4\right )+c_2 \operatorname {hypergeom}\left (\left [2\right ], \left [\frac {2}{3}\right ], \frac {x^{3}}{3}\right ) {\mathrm e}^{-\frac {x^{3}}{3}} \]

✓ Mathematica. Time used: 0.25 (sec). Leaf size: 69

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

\begin{align*} y(x)&\to \frac {1}{36} \left (36 c_1 x \left (x^3+4\right )-3 c_2 e^{-\frac {x^3}{3}} \left (x^3+3\right )+3^{2/3} c_2 \sqrt [3]{x^3} \left (x^3+4\right ) \Gamma \left (\frac {2}{3},\frac {x^3}{3}\right )\right ) \end{align*}

✗ Sympy

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

False