Show that all solutions of differential equation $$ x' = \left( \frac{x^2+1}{t^4+1} \right)^{1/3}$$ have two horizontal asymptotes.
Obviously, the derivative is positive everywhere, so it is sufficient to show that all solutions are bounded. However, i have no clue how to do that.
Hint: separate the variables. Send $t\to\infty$. Observe that one of the integrals converges. Conclude. Send $t\to-\infty$...