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

Question

5813 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-09T17:24:19

$y = (2-Ce^{-6x})/3$

this is separable

$dy/dx=4-6y$

$1/(4-6y) dy/dx=1$

we integrate both sides

$int 1/(4-6y) dy/dx \ dx=int \ dx$

or

$int 1/(4-6y) dy =int \ dx$

$- 1/6 ln(4-6y) =x + C$

please note that I am using C as a generic constant here so it's value changes through the process

$ln(4-6y) = C - 6x$

$4-6y = e^{C - 6x} = e^C e^{-6x} = Ce^{-6x}$

$y = (2-Ce^{-6x})/3$

please note that I am using C as a generic constant here so it's value changes through the process

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