83.41.12 problem 3

Internal problem ID [19413]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise at end of chapter VIII. Page 141
Problem number : 3
Date solved : Thursday, March 13, 2025 at 02:24:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x \left (-x^{2}+1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) \left (3 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=x*(-x^2+1)^2*diff(diff(y(x),x),x)+(-x^2+1)*(3*x^2+1)*diff(y(x),x)+4*x*(x^2+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \left (x^{2}-1\right ) \left (c_{2} \ln \left (x \right )+c_{1} \right ) \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 20

ode=x*(1-x^2)^2*D[y[x],{x,2}]+(1-x^2)*(1+3*x^2)*D[y[x],x]+(4*x)*(1+x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\left (\left (x^2-1\right ) (c_2 \log (x)+c_1)\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x**2)**2*Derivative(y(x), (x, 2)) + 4*x*(x**2 + 1)*y(x) + (1 - x**2)*(3*x**2 + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False