Question: Defining boundary conditions for ODE

I want to solve the following ode: 

ode := diff(x(t), t) = k*(a - x(t))*(b - 2*x(t))^2

k, a and b are positive real numbers and I want to add the condition that a-x(t) >= 0 and b-2x(t) >=0, in addition to x(0)=0

how to I do that?

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