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

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Answer 1 · 2016-07-11T20:45:31

#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#