23.1.381 problem 366

Internal problem ID [4988]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 366
Date solved : Tuesday, September 30, 2025 at 09:08:56 AM
CAS classification : [_rational, _Riccati]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

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

\[ y = \frac {c_1 \operatorname {EllipticCE}\left (x \right )+\operatorname {EllipticE}\left (x \right )-\operatorname {EllipticK}\left (x \right )}{c_1 \operatorname {EllipticCE}\left (x \right )-c_1 \operatorname {EllipticCK}\left (x \right )+\operatorname {EllipticE}\left (x \right )} \]

✓ Mathematica. Time used: 0.563 (sec). Leaf size: 91

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

\begin{align*} y(x)&\to -\frac {2 \left (\pi G_{2,2}^{2,0}\left (x^2| \begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,1 \\ \end {array} \right )+c_1 \left (\operatorname {EllipticK}\left (x^2\right )-\operatorname {EllipticE}\left (x^2\right )\right )\right )}{\pi G_{2,2}^{2,0}\left (x^2| \begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\ \end {array} \right )+2 c_1 \operatorname {EllipticE}\left (x^2\right )}\\ y(x)&\to 1-\frac {\operatorname {EllipticK}\left (x^2\right )}{\operatorname {EllipticE}\left (x^2\right )} \end{align*}

✗ Sympy

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

TypeError : bad operand type for unary -: list