1. Mimi_x3
2. anonymous

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

3. Mimi_x3

:|

4. Mimi_x3

give me a sec

5. Mimi_x3

6. anonymous

Sure you know that you need a substitution, right?

7. Mimi_x3

what substitution

8. 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 $$y$$

9. Mimi_x3

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

10. Mimi_x3

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

11. anonymous

let $$y_1=x_1$$ and $$y_2=x_1+x_2$$ see what happens

12. Mimi_x3

do i sub it into x dot?

13. anonymous

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

14. anonymous

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

15. Mimi_x3

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

16. anonymous

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

17. Mimi_x3

dx/dt ?

18. anonymous

exactly

19. anonymous

Now, what about $$\dot{y_2}$$ ?

20. Mimi_x3

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

21. 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.

22. 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

23. 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

24. anonymous

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

25. Mimi_x3

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

26. Mimi_x3

y dot = -(2x_1+x_2)

27. Mimi_x3

28. anonymous

ok, let me explain it step by step

29. anonymous

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

30. anonymous

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

31. 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$

32. Mimi_x3

how would you know what sub to do

33. anonymous

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

34. Mimi_x3

by looking

35. Mimi_x3

thanks

36. anonymous

No problem, skill develops with practice and experience

37. Jack1

nice