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

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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