# Consider the differential equationdy/dt = y−y2.Given that y(0)=0.5, solve the differential equation by separating the variables and integrating. Given thaty→L as t→∞,for some constant L, find the value of L. Hint: You may use the fact that1x(1−x)≡1x+11−x.

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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.

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Step 1

To find the expression for y(t) and find the limit y(t) as t tends to infinity

Step 2

Separate the variables and use partial fractions. As the denominator is not defined at y=1 , we need to discuss the cases y<1 and y>1 separately

Step 3

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### Calculus 