# Consider the differential equation dy/dt = y−y2. Given that y(0)=0.5, solve the differential equation by separating the variables and integrating. Given that y→L as t→∞, for some constant L, find the value of L.   Hint: You may use the fact that 1x(1−x)≡1x+11−x.

Question

Consider the differential equation

dy/dt = y−y2.

Given that y(0)=0.5, solve the differential equation by separating the variables and integrating. Given that

y→L as t→∞,

for some constant L, find the value of L.

Hint: You may use the fact that

1x(1−x)≡1x+11−x.