23.3.494 problem 500

Internal problem ID [6208]
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 : 500
Date solved : Tuesday, September 30, 2025 at 02:36:21 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 4 x y-\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 33

ode:=4*x*y(x)-(x^2+7)*diff(y(x),x)+x*(-x^2+1)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{8}+6 c_2 \,x^{4}-8 c_2 \,x^{2}+3 c_2}{\left (x^{2}-1\right )^{3}} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 42

ode=4*x*y[x] - (7 + x^2)*D[y[x],x] + x*(1 - x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-24 c_1 x^8+6 c_2 x^4-8 c_2 x^2+3 c_2}{24 \left (x^2-1\right )^3} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x**2)*Derivative(y(x), (x, 2)) + 4*x*y(x) - (x**2 + 7)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None