Chapter 5.4, Problem 2E

In Problems 1 and 2, verify that pair $x\left(t\right)$, $y\left(t\right)$ is a solution to the given system. Sketch the trajectory of the given solution in the phase plane.

$\frac{dx}{dt}=1$, $\frac{dy}{dt}=3x^2$;

$x\left(t\right)=t+1$, $y\left(t\right)=t^3+3t^2+3t$