# What is a solution to the differential equation dy/dx=4−6y?

What is a solution to the differential equation $\frac{dy}{dx}=4-6y$?
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Mekhi Parker
this is separable
$\frac{dy}{dx}=4-6y$
$\frac{1}{4-6y}\frac{dy}{dx}=1$
we integrate both sides

or

$-\frac{1}{6}\mathrm{ln}\left(4-6y\right)=x+C$
please note that I am using C as a generic constant here so it's value changes through the process
$\mathrm{ln}\left(4-6y\right)=C-6x$
$4-6y={e}^{C-6x}={e}^{C}{e}^{-6x}=C{e}^{-6x}$
$y=\frac{2-C{e}^{-6x}}{3}$
please note that I am using C as a generic constant here so it's value changes through the process