Nonlinear autonomous system of differential equation

Question

I have the following differential system :

$x' = \frac {x^2}{(y-1)}$

$y' = x+1$

By elimination method things get ugly, so how could I solve it?

Answer 1

i dont know if this helps but i can find a relationship between $x$ and $y.$

you can split this up into two decoupled equations $$\frac{dx}{ds} = \frac{x^2}{x+1}, \frac{dy}{ds} = y-1 $$ this has the solution $$y = 1+ce^s,s = \ln x -\frac1x + d $$