# What is a solution to the differential equation #dx/dt=t(x-2)# with x(0)=5?

This is a First Order separable DE, so we can "separate the variables" to get;

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The solution to the differential equation ( \frac{dx}{dt} = t(x-2) ) with ( x(0) = 5 ) is ( x(t) = 2t^2 + 3t + 5 ).

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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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