Question

Verify that the logistic differential equation
dy/dt =4y(1−y)
has solution
y(t) =1/1 + ce−4t
(for any value of the constant c) by substituting into the differential equation.

Answer 1

So you do not have to solve the equation.
You can verify by differentiating the function y(t), giving you y'(t).
Now, with y(t) do the calculation that is on the right hand side of the equation.
If this gives the same result as y'(t), you're safe!