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

Answer 1

Luke Alvarez

#x = C e^{ t^2 /2} + 2#

this is separable

#dx/dt=t(x-2)#

#1/(x-2) \ dx/dt=t#

#int \ 1/(x-2) \ dx/dt \ dt =int \ t \ dt#

#int \ 1/(x-2) \ dx =int \ t \ dt#

#ln(x-2) = t^2 /2 + C#

#x-2 = e^{ t^2 /2 + C} = C e^{ t^2 /2}#

#x = C e^{ t^2 /2} + 2#

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Answer 2

Scarlett Allison

The solution to the differential equation dx/dt = t(x - 2) is given by:

x(t) = Ce^(t^2/2) + 2

where C is the constant of integration.

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Answer from HIX Tutor

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.