How do I solve the equation $dy/dt = 2y - 10$ ?

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Answer 1 · 2015-01-31T20:07:21

You can use a technique known as Separation of Variables.
Take all the $y$ to one side and the $t$ on the other...
You get:

$dy/(2y-10)=dt$

Now you can integrate both sides with respect to the correspondent variables:

$int1/(2y-10)dy=intdt$
$int1/(2(y-5))dy=intdt$

And finally
$1/2ln(y-5)=t+c$

Now you can express $y$ as:
$ln(y-5)=2t+c$
$y-5=c_1e^(2t)$ where $c_1=e^c$
$y=c_1e^(2t)+5$

You can substitute back to check your result (calculating $dy/dt$ ) remembering that now it is: $y=c_1e^(2t)+5$

How do I solve the equation dy/dt = 2y - 10dy/dt = 2y - 10?