How can I get a conserved quantity if I have an autonomous system

Given: Functions x(t), y(t)
Let my autonomous system be

dx(t)/dt=(y(t))^2
dy(t)/dt=(x(t))^3

Now... how can I find out what the conserved quantity is?

I really hope someone can help me here :)

dy/dx = x³/y²
∫y²dy = ∫x³dx
y³/3 = x⁴/4 + C
=> y³/3 - x⁴/4 = const
the conserved quantity is y³/3 - x⁴/4 or 4y³ - 3x⁴