23.3.503 problem 509

Internal problem ID [6217]
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 : 509
Date solved : Tuesday, September 30, 2025 at 02:36:34 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} -6 x y-y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \end{align*}

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

ode:=-6*x*y(x)-diff(y(x),x)+x*(x^2+2)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x^{2}+2\right )^{{3}/{4}} \left (x^{{3}/{2}} c_1 +\operatorname {hypergeom}\left (\left [-\frac {3}{4}, \frac {7}{4}\right ], \left [\frac {1}{4}\right ], -\frac {x^{2}}{2}\right ) c_2 \right ) \]

✓ Mathematica. Time used: 0.145 (sec). Leaf size: 54

ode=-6*x*y[x] - D[y[x],x] + x*(2 + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{6} \left (x^2+2\right )^{3/4} \left (6 c_1 x^{3/2}-\sqrt [4]{2} c_2 \operatorname {Hypergeometric2F1}\left (-\frac {3}{4},\frac {7}{4},\frac {1}{4},-\frac {x^2}{2}\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**2 + 2)*Derivative(y(x), (x, 2)) - 6*x*y(x) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False