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

- Mimi_x3

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

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- Mimi_x3

https://gyazo.com/b7c760976b5d45ae89ade505c11949ff

- anonymous

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

- Mimi_x3

:|

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## More answers

- Mimi_x3

give me a sec

- Mimi_x3

##### 1 Attachment

- anonymous

Sure you know that you need a substitution, right?

- Mimi_x3

what substitution

- anonymous

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 \(y\)

- Mimi_x3

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

- Mimi_x3

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

- anonymous

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

- Mimi_x3

do i sub it into x dot?

- anonymous

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

- anonymous

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

- Mimi_x3

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

- anonymous

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

- Mimi_x3

dx/dt ?

- anonymous

exactly

- anonymous

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

- Mimi_x3

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

- UsukiDoll

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.

- anonymous

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

- anonymous

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

- anonymous

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

- Mimi_x3

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

- Mimi_x3

y dot = -(2x_1+x_2)

- Mimi_x3

yeah my bad

- anonymous

ok, let me explain it step by step

- anonymous

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

- anonymous

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

- anonymous

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

- Mimi_x3

how would you know what sub to do

- anonymous

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

- Mimi_x3

by looking

- Mimi_x3

thanks

- anonymous

No problem, skill develops with practice and experience

- Jack1

nice

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