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

tophergopher3wo 2022-09-14 Answered
What is a solution to the differential equation d y d x = 4 - 6 y ?
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Answers (1)

Mekhi Parker
Answered 2022-09-15 Author has 18 answers
this is separable
d y d x = 4 - 6 y
1 4 - 6 y d y d x = 1
we integrate both sides
1 4 - 6 y d y d x   d x =   d x
or
1 4 - 6 y d y =   d x
- 1 6 ln ( 4 - 6 y ) = x + C
please note that I am using C as a generic constant here so it's value changes through the process
ln ( 4 - 6 y ) = C - 6 x
4 - 6 y = e C - 6 x = e C e - 6 x = C e - 6 x
y = 2 - C e - 6 x 3
please note that I am using C as a generic constant here so it's value changes through the process

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