How do I solve this equation dy/dx=5-y?

Question

This is a differential equation

Answer 1

You separate the variables to get:

1/(5-y) dy = dx

then you intergate each side:

-ln (5-y) = x + c

Solve for y:

ln(5-y) = -x + C

5-y = Ce^-x

y = Ce^-x + 5

note, the C's were changing in the solving process, but still an arbitrary constant.

Answer 2

Make 2 fraction bars ex) / = /
Make the 5-y over 1 5-y/1
Create LCD /DX /DX Since dx seems to b the LCD DY carries over
DY/DX=5-y/DX Cross out the D and make a equation
DY= 5-Y Subtract the why on the left to X it out and do it the same on the right. D = 5
Whenever it is a = The answer is a variable to a number

Answer 3

dx=dy/(5-y)
x= - ln(5-y)+C