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

Question

10505 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-11T20:45:31

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

this is separable

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

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

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

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

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

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

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

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