Question

t^2dy/dt+2ty-y^5=0,t>0 solve the bernoulli equation by using a substitution v=y^1-n

Answer 1

can any one help me plz

Answer 2

ok, first of all, you need your first fan

Answer 3

above is the question

Answer 4

hmm... let me think

Answer 5

ok

Answer 6

nah, sorry, TOO hard for me, cant figure it out, I am not good with those derivatives and stuff, sorry....

Answer 7

ok

Answer 8

BTW, did you try google?

http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/ode/first/bernoulli/bernoulli.html

http://tutorial.math.lamar.edu/Classes/DE/Bernoulli.aspx

http://www.sosmath.com/diffeq/first/bernouilli/bernouilli.html

???

Answer 9

you want to derive it?

Answer 10

yes

Answer 11

is the question:\[dy/dt (t^2 +2ty - y^5)\]?

Answer 12

yes

Answer 13

using v = y - n?

Answer 14

i need to solve it by bernoulli equation substitution method

Answer 15

v=y^1-n

Answer 16

yes

Answer 17

you can take y = v + n

Answer 18

substitute Y in the equation and you'll get :\[t^2 + 2t(v+n) - (v+n)^5\]

Answer 19

ok

Answer 20

you want to derive with respect to t?

Answer 21

yes

Answer 22

then you'll treat (v+n) in the equation as constants

Answer 23

and so, I think you'll get :

= 2t + 2(v+n) -(v +n)
= 2t +2v + 2n -v -n
= 2t +v +n

I guess :)

Answer 24

since you're deriving with respect to t, then you'll ignore the others and treat them as constants.

please correct me if I'm wrong

Answer 25

y and v are functions of t though. Also, yummy the site andrius gave you it awesome and easy to read

Answer 26

lol yeah, google it :)