$\backslash [$

$\backslash$frac$\{\backslash$mathrm$\{$dx$\}\}\{\backslash$mathrm$\{$dt$\}\}=\backslash$mathrm$\{$x$\}^\{2\}-196$

$\backslash ]$

Identify all of the stable critical points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The given differential equation has $($a$)$ stable critical point$($s$)$ at $\backslash ($ x$=\backslash$square $\backslash ).$

$($Simplify your answer. Use a comma to separate answers as needed.$)$

B$.$ The given differential equation has no stable critical point. Identify all of the unstable critical points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The given differential equation has $($an$)$ unstable critical point$($s$)$ at $\backslash ($ x$=\backslash )$

$($Simplify your answer. Use a comma to separate answers as needed.$)$

$3.$ The given differential equation has no unstable critical point.

Identify all of the semi$-$stable critical points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The given differential equation has $($a$)$ semi$-$stable critical point$($s$)$ at $\backslash ($ x$=18\backslash ).$

$($Simplify your answer. Use a comma to separate answers as needed.$)$

B$.$ The given differential equation has no semi$-$stable critical point.

Construct the phase diagram. Choose the correct phase diagram below.

B$.$

Solve the differential equation using the initial condition $\backslash ($ x$(0)=$x$\_\{0\}\backslash ).$

$\backslash [$

x$($t$)=\backslash$frac$\{(18$ t$-1)$ x$\_\{0\}-324$ t$\}\{$t x$\_\{0\}-18$ t$-1\}$

$\backslash ]$

Sketch the solution curves. Choose the correct answer below.