Question

hey can someone please give me COMPLETE step by step instructions on how to seperate the varialbes in this DE: dy/dx = (1+2y^2)/(ysinx)

Answer 1

is this implicit differentiation

Answer 2

I don't know..I'm in calc 2, were studying very basic DE's. It just says SOLVE. I know how to solve it, i just don't know how i can seperate the variables in this equation.

Answer 3

Once i seperate the variables it is very easy to solve...but i dont know how to seperate the variables...

Answer 4

dy/dx[1]+dy/dx[2y^2] all divided by dy/dx[ysinx]

Answer 5

and your solving for y

Answer 6

I dont get it...I dont need the answer, I want to learn how to seperate the variables

Answer 7

thats not the answer that how you seperate them

Answer 8

you will also be using the quotient rule which is fg'-gf'/g^2

Answer 9

I dont understand...Can you tell me step by step what i should do, i will work out out on my paper. For example say "first you must move the y to the left by multipying both sides by y) be very specific please...i know the answer i just dont get how to get there!

Answer 10

and go ONE step at a time, very slowly

Answer 11

i will try and help as much as i can but am studying calc 1 and am not that good at this

Answer 12

Oh ok well what i am asking is just algebraic manupulation..how can i move all the y's to one side and x's to the right

Answer 13

ok so this is definitely imlicit

Answer 14

yeah am stuck an sorry

Answer 15

fine.. so you seperate variables
get ydy/(1+2y^2) = (sinx)^-1 dx right?

Answer 16

look at the left side use substitution: say u=1+2y^2 so du=4ydy but as you have y not 4y you take 1/4 outside of the integral which gives you int(du/u) which is lnu which is ln(1+2y^2)

Answer 17

so the right side: integral of cscx is -ln(cot(x)+csc(x)) + C and as we have a ln on both sides we can take do e^ln(...) which negates the ln(...) on both sides

Answer 18

this gives us 1+2y^2 = K(cotx +cscx) so y= sqrt(K(cotx +cscx) -1)/2)

Answer 19

on second thought this may actually be totally wrong but check it for yourself