54.1.248 problem 253

Internal problem ID [11562]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 253
Date solved : Tuesday, September 30, 2025 at 09:18:55 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8&=0 \end{align*}

✗ Maple

ode:=(x^2*y(x)-1)*diff(y(x),x)+8*x*y(x)^2-8 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x^2*y[x]-1)*D[y[x],x]+8*(x*y[x]^2-1)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x*y(x)**2 + (x**2*y(x) - 1)*Derivative(y(x), x) - 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out