Mimi_x3
  • Mimi_x3
help pls...i have no clue about this course
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Mimi_x3
  • Mimi_x3
https://gyazo.com/b7c760976b5d45ae89ade505c11949ff
anonymous
  • anonymous
I can't open it, seems I need a proxy
Mimi_x3
  • Mimi_x3
:|

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Mimi_x3
  • Mimi_x3
give me a sec
Mimi_x3
  • Mimi_x3
anonymous
  • anonymous
Sure you know that you need a substitution, right?
Mimi_x3
  • Mimi_x3
what substitution
anonymous
  • 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
  • Mimi_x3
I really don't know...can you please elaborate
Mimi_x3
  • Mimi_x3
I can't find anything related to this on google :/
anonymous
  • anonymous
let \(y_1=x_1\) and \(y_2=x_1+x_2\) see what happens
Mimi_x3
  • Mimi_x3
do i sub it into x dot?
anonymous
  • 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
  • anonymous
Hey dont overthink it, this is just some algebraic manipulation, Its not weird
Mimi_x3
  • Mimi_x3
I don't get it why does y dot = x dot?
anonymous
  • anonymous
Its a dynamical system, dot is "derivative with respect to time" here
Mimi_x3
  • Mimi_x3
dx/dt ?
anonymous
  • anonymous
exactly
anonymous
  • anonymous
Now, what about \(\dot{y_2}\) ?
Mimi_x3
  • Mimi_x3
I don't get how the x is related to the y?
UsukiDoll
  • 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
  • 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
  • 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
  • anonymous
And x is not related to y, we relate it to y :)
Mimi_x3
  • Mimi_x3
i don't get it y dot = -(2x + x)
Mimi_x3
  • Mimi_x3
y dot = -(2x_1+x_2)
Mimi_x3
  • Mimi_x3
yeah my bad
anonymous
  • anonymous
ok, let me explain it step by step
anonymous
  • anonymous
you have these system of equations:\[\dot{x_1}=x_1+x_2 \]\[\dot{x_2}=-2x_1-x_2\]
anonymous
  • 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
  • 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
  • Mimi_x3
how would you know what sub to do
anonymous
  • anonymous
that's just like integrals, how do you solve integrals with u-sub?
Mimi_x3
  • Mimi_x3
by looking
Mimi_x3
  • Mimi_x3
thanks
anonymous
  • anonymous
No problem, skill develops with practice and experience
Jack1
  • Jack1
nice

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