Question

help pls...i have no clue about this course

Answer 1

https://gyazo.com/b7c760976b5d45ae89ade505c11949ff

Answer 2

I can't open it, seems I need a proxy

Answer 3

:|

Answer 4

give me a sec

Answer 5

Sure you know that you need a substitution, right?

Answer 6

what substitution

Answer 7

sub \(y_1=f(x_1, x_2)\) and \(y_2=g(x_1, x_2)\) in a way that first two equations turn into second system in terms of \(y\)

Answer 8

I really don't know...can you please elaborate

Answer 9

I can't find anything related to this on google :/

Answer 10

let \(y_1=x_1\) and \(y_2=x_1+x_2\) see what happens

Answer 11

do i sub it into x dot?

Answer 12

sry, I was out, see for example\[\dot{y_1}=\dot{x_1}=x_1+x_2=y_2\]Now you calculate \(\dot{y_2}\)

Answer 13

Hey dont overthink it, this is just some algebraic manipulation, Its not weird

Answer 14

I don't get it
why does y dot = x dot?

Answer 15

Its a dynamical system, dot is "derivative with respect to time" here

Answer 16

dx/dt ?

Answer 17

exactly

Answer 18

Now, what about \(\dot{y_2}\) ?

Answer 19

I don't get how the x is related to the y?

Answer 20

the dot isn't used that much , but it's another way of saying first derivative for a single dot
2nd derivative for a double dot.

Answer 21

That depends on how we define y in terms of x, we do this sub to get a simpler form of equations that are easy to interpret physically

Answer 22

Think of it like this, you have a system of differential equations in x_1 and x_2 and you wanna solve it, you do a sub to get a simpler form and to solve it more easily

Answer 23

And x is not related to y, we relate it to y :)

Answer 24

i don't get it
y dot = -(2x + x)

Answer 25

y dot = -(2x_1+x_2)

Answer 26

yeah my bad

Answer 27

ok, let me explain it step by step

Answer 28

you have these system of equations:\[\dot{x_1}=x_1+x_2 \]\[\dot{x_2}=-2x_1-x_2\]

Answer 29

Now I do a sub in the form \(y_1=x_1\) and \(y_2=x_1+x_2\), lets see what happens

Answer 30

\[\dot{y_1}=\dot{x_1}=x_1+x_2=y_2\]\[\dot{y_2}=\dot{x_1}+\dot{x_2}=x_1+x_2-2x_1-x_2=-x_1=-y_1\]

Answer 31

how would you know what sub to do

Answer 32

that's just like integrals, how do you solve integrals with u-sub?

Answer 33

by looking

Answer 34

thanks

Answer 35

No problem, skill develops with practice and experience

Answer 36

nice