Question

does anyone know how to simplify around y the expression dy/dt = -67.1(y/12200) + 550

Answer 1

is this a separable equation?

Answer 2

yes it is

Answer 3

its a differential equation

Answer 4

\[\frac{ dy }{ dt }=\frac{ -67.1y }{ 12200 }+550=\frac{ -67.1y }{ 12200 }+\frac{ 6710000 }{ 12200 }=\frac{ -67.1y+6710000 }{ 12200 }\]\[\implies \frac{ dy }{ -67.1+6710000 }=\frac{ dt }{ 12000 }\]\[\int\limits_{}^{}\frac{dy }{ -67.1y + 6710000 }=\int\limits_{}^{}\frac{ dt }{ 12000 } \] From here, just solve the separable differentiate equation for y which is pretty straight forward.

@isai