the books shows answer like this

a=dv/dt

16-4v=dv/dt

4(4-v)=dv/dt

-4dt=dv/(v-4) <- integrating both

-4t + C = ln v-4 then determine C by given condition

(t=0 v=5)

C = ln 1 = 0

then v = 4 + e^-4t is the general equation ###book ans###

and my attempt is not simplify the 16-4v to 4(4-v)

but just leave it as 16-4v but it don't give same result

here my attempt

a=dv/dt

16-4v=dv/dt

-dt=dt/(4v-16) then integrating both side

-t + C= ln (4v -16) determine value of C

(when t=0 v=5)

C = ln 4 then back to

-t + ln 4 = ln (4v - 16) or i can write it as

-t = ln(4v - 16) - ln 4 and by logaritm properties is turned to

-t = ln ((4v-16)/4)

4e^-t = 4v -16 simplyfied

4 + e^-t = v ###mine###

There is significant difference between both result, so i hope anyone can show me where did i go wrong