23.3.371 problem 375

Internal problem ID [6085]
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 : 375
Date solved : Tuesday, September 30, 2025 at 02:21:13 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} -4 y-6 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

ode:=-4*y(x)-6*x*diff(y(x),x)+(-x^2+1)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 44

ode=-4*y[x] - 6*x*D[y[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 {3 c_1-c_2 x \left (x^2-3\right )}{3 \sqrt {1-x^2} \left (x^2-1\right )^{3/2}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x*Derivative(y(x), x) + (1 - x**2)*Derivative(y(x), (x, 2)) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False