Question

is it possible to use Laplace transformations on first order differential equations?

Answer 1

it is

Answer 2

could you show me a demonstration?

for example...

(x^2-y)y' + 2x^3 +2xy = 0

Answer 3

it is not

Answer 4

uhh so which is it?

Answer 5

emm...can we evaluate L{yy'} ?

Answer 6

i have no idea...can we?

Answer 7

http://www.wolframalpha.com/input/?i=laplace+transform++of++y%28t%29y%27%28t%29

Answer 8

we cant

Answer 9

aww so laplace transform is only possible in higher order diff eqs?

Answer 10

not necessarily

Answer 11

well its not the order here, is it? we could still use LT on y` = cos(x). this is 1st order

Answer 12

its not the order that is the problem*

Answer 13

you can do laplace on things with x? i thought you can only use it on t

Answer 14

where x = t

Answer 15

so laplace of that is

sy(s) - y(0) = s/(s^2 + k^2)

??

Answer 16

looks right to me

Answer 17

yes had to check the old LT notes.

Answer 18

so what happens after that?

Answer 19

wait it should be y(t)

Answer 20

then you would solve for y(t) and then try and find some inverse from a table of inverses that would help you solve

Answer 21

I think.. its been a bit. one sec

Answer 22

s*L(y(t)) - y(0) = s/(s^2 + 1^2)

Answer 23

solve for L(y(t)) then take the inverse of both sides. no we will have some y(t) = L^(-1)(...) then you use a table of iverses. Most of the time you need ot do some algebra magic to get it to work out.

Answer 24

lol. i guess sticking to the traditional way is better?

Answer 25

well, sometimes not. most of the time yes.

Answer 26

thought I should do it since I could not remember how

Answer 27

its good for dirac delta function, stuff like that