$11.$ For the differential equation x$\text{'}=$ x$^3,$

$($a$)$ Show that x$($t$)=$ sqrt$(1/($C$-2$t$))$

$($b$)$ Find one solution of x$\text{'}=$ x$^3$ that cannot be written in this form for any value of C$.$

$($c$)$ Find the solution satisfying the initial condition x$(0)=1,$ and sketch its graph.

$($d$)$ Does the solution in part $($c$)$ have a vertical asymptote? If so$,$ for what value of t$?$