Question

dy/dx = 4y/(x+3)
I need to find the anti-derivative of that, pwease help :3

Answer 1

divide both side by y and multiply both sides by dx

Answer 2

then integrate both sides. Done

Answer 3

dy/y = 4dx / (x+3) ? so that becomes lny on the left
but idk about the right side...

Answer 4

it's just integrating 4/(x+3) dx

Answer 5

so lny = 4ln(x+3) ?

Answer 6

lny = 4ln(x+3) + C

Answer 7

oh right plus C :P
and how do I solve for y? ...
divide both sides by ln?

Answer 8

XDDDD!!! sorry i just have to laugh a little. you can't dividing both sides by just ln!! it's like dividing both sides by just a square root sign!!

Answer 9

:P yeah... I kinda might have missed the log lesson xD

Answer 10

ln(y) = x means y = e^x

Answer 11

so y = e^(4ln(x+3) + C) ?

Answer 12

right

Answer 13

y = e^(4ln(x+3)) * e^(c) = C e^(4ln(x+3)) ? what else?

Answer 14

n ln(x) = ln(x^n)

Answer 15

so I should bring the 4 up like
y = C e^(ln((x+3)^4)) ?

Answer 16

and e^ln(x) = x

Answer 17

so y = C (x+3)^4 ?

Answer 18

bingo

Answer 19

Alright :D Thank you!!! ^_^

Answer 20

yw