Question

What is the answer to this (Differential Equations): http://img594.imageshack.us/img594/8306/math1d.png

Answer 1

this is a seperable integration put the y's on one side and x's on another so our integral would be dy/y = 6 dx now if we integrate both sides we achieve lny = 6x +c now to use our y(0)=3 to find c

therefore y=3 and x =0 lets plug it into our equation to get ln3 = 6(0) + c --> c=ln3

therefore lny = 6x + ln3 now to find y(-ln3/3) this implies lny = 6(-ln3/3) + ln3 --> ln y = -2ln3 + ln3 --> lny=-ln3 --> lny = ln 3^-1 now raise both sides by e to achieve

y = 3^-1 = 1/3 :)

Answer 2

first separate variables
dy/dx = 6y
dy
-- = 6 dx
y

hamza has it

Answer 3

I tried this problem out, and when I did it, I made the LS containing values with y, include the 6 as well. So I had:

(1/6y)dy

Answer 4

Why is it wrong to carry that 6 over?

Answer 5

are you sure about that? hmm strange let me try it out

Answer 6

you shouldnt get a different answer you made a calculating error

Answer 7

because notice when you are integrating that you take the constant out (1/6) first then integrate 1/y and then you have to multiply it by 6 again you know

Answer 8

So I would get

6lny = x+ c?

Answer 9

no you would get (1/6)lny = x+c

Answer 10

ohhh, okay yeah that explains it all. thanks, i understand your answer and my error now

Answer 11

awesome goodluck :)

Answer 12

thanks!