# What is the solution of the differential equation # dy/dx = 2y(5-3y) # with #y(0)=2#?

# y = (10e^(10x))/(6e^(10x)-1) #

We have:

We can "separate the variables" in this First Order Separable ODE to obtain

By breaking down the integrand into partial fractions, it is possible to integrate the LHS while the RHS remains trivial.

Getting to the answer:

Thus, we can now write:

And after integrating, we obtain:

Thus, we have:

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This differential equation can be separated:

Then, the necessary resolution is:

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The solution to the given differential equation ( \frac{dy}{dx} = 2y(5 - 3y) ) with the initial condition ( y(0) = 2 ) is:

[ y(x) = \frac{5e^{10x}}{3e^{10x} + 1} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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