$($a$)$ Solve $($dx$)/($dt$)=($x$^(2)-1)$t$.$

Use C for the arbitrary constant. Use exp for the exponential function. For example, exp$(3^(**)$t$)$ for e$^(3$t$).$

Hint: Expand x$-$integrand as partial fractions. Be careful with absolute values.

x$($t$)=$

$($b$)$ What is the solution with x$(0)=(13)/(11)($which is about $1\mathrm{.}1818181818181819).$

x$($t$)=|$

$\backslash$int x

$($c$)$ What is the t$-$interval on which your solution in part $($b$)$ exists?

Use standard interval notation: for example $(3,7]$ to mean log$()3.$

Use log$()$ for the natural logarithm.

$($d$)$ Which family in the picture does your solution in part $($b$)$ belong to$?$