29.20.19 problem 566

Internal problem ID [5160]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 566
Date solved : Sunday, March 30, 2025 at 06:46:10 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 951

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 34.122 (sec). Leaf size: 506

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

\begin{align*} y(x)\to \frac {\sqrt [3]{-(1-6 c_1){}^2 x^3+\sqrt {(-1+6 c_1){}^3 \left (6 c_1 x^6+(2-12 c_1) x^3-1+6 c_1\right )}+1+36 c_1{}^2-12 c_1}}{-1+6 c_1}-\frac {x^2}{\sqrt [3]{-(1-6 c_1){}^2 x^3+\sqrt {(-1+6 c_1){}^3 \left (6 c_1 x^6+(2-12 c_1) x^3-1+6 c_1\right )}+1+36 c_1{}^2-12 c_1}}+x \\ y(x)\to \frac {i \left (\sqrt {3}+i\right ) \sqrt [3]{-(1-6 c_1){}^2 x^3+\sqrt {(-1+6 c_1){}^3 \left (6 c_1 x^6+(2-12 c_1) x^3-1+6 c_1\right )}+1+36 c_1{}^2-12 c_1}}{-2+12 c_1}+\frac {\left (1+i \sqrt {3}\right ) x^2}{2 \sqrt [3]{-(1-6 c_1){}^2 x^3+\sqrt {(-1+6 c_1){}^3 \left (6 c_1 x^6+(2-12 c_1) x^3-1+6 c_1\right )}+1+36 c_1{}^2-12 c_1}}+x \\ y(x)\to -\frac {i \left (\sqrt {3}-i\right ) \sqrt [3]{-(1-6 c_1){}^2 x^3+\sqrt {(-1+6 c_1){}^3 \left (6 c_1 x^6+(2-12 c_1) x^3-1+6 c_1\right )}+1+36 c_1{}^2-12 c_1}}{-2+12 c_1}+\frac {\left (1-i \sqrt {3}\right ) x^2}{2 \sqrt [3]{-(1-6 c_1){}^2 x^3+\sqrt {(-1+6 c_1){}^3 \left (6 c_1 x^6+(2-12 c_1) x^3-1+6 c_1\right )}+1+36 c_1{}^2-12 c_1}}+x \\ y(x)\to x \\ \end{align*}

✗ Sympy

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

Timed Out