The system

$x^{\text{'}}=-y$

$y^{\text{'}}=-y-x(x-0\mathrm{.}15)(x-2),>0$

results from an approximation to the Hodgkin$-$Huxley equations, which model the transmission of neural impulses along an axon. Consider the trajectory that

leaves the critical point $(2,0).$ Find the value of $$ for which this trajectory ultimately approaches the origin as

Answer: