60.1.247 problem 252

Internal problem ID [10261]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 252
Date solved : Sunday, March 30, 2025 at 03:35:10 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 951

ode:=(x^2*y(x)-1)*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: 6.921 (sec). Leaf size: 127

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

\[ \text {Solve}\left [\int _1^x\frac {2 \sqrt [3]{2} 5^{2/3} \left (-\frac {1}{K[2]^3}\right )^{2/3} K[2]}{9 \left (K[2]^3-1\right )}dK[2]+c_1=\int _1^{\frac {3 x^3-4 y(x) x^2+1}{2^{2/3} \sqrt [3]{5} \sqrt [3]{-\frac {1}{x^3}} x \left (x^2 y(x)-1\right )}}\frac {1}{K[1]^3+\frac {21 \sqrt [3]{-\frac {1}{2}} K[1]}{2\ 5^{2/3}}+1}dK[1],y(x)\right ] \]

✗ 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