So I need to solve this differential equation

Question

dy/dx = 1/(x+2)

so i solved it like this

dy = 1/(x+2)dx

then i took the integral of both sides

y= ⌠1/(x+2)dx
⌡
then performed a u sub

u = x+2

du = 1dx

y = ⌠du/u
⌡
y = ln abs(u)+c

y = ln abs(x+2)+c

but the sanswer is supposed to be

y = ln abs ((x+2)/2) + c

Where did I mess up? and where did the 2 in the denominatior of the (x+2) come from?

Answer 1

Not sure where the 2 came from, but since

ln(u/2) = ln(u) - ln(2)

just fold the ln(2) into the C.

Answer 2

okay thank you!

Answer 3

i don't know answer.i am tring to find answer