find the function fx passing through the point 06 that has t

find the function f(x) passing through the point (0,6) that has the first derivative dy/dx=(y-2)

Solution

dy/dx=y-2

dy/y-2=dx

integrating both sides

ln(y-2)=x+c

as line passes through(0,6)

ln(6-2)=0+c

c=ln(4)

ln(y-2)=x+ln4

x=ln(y-2/4)