anonymous one year ago Differential equations question !

1. anonymous

$3\frac{d^3y(t)}{ dt }+\frac{ dy(t) }{ dt }+2y(t)=u(t)$

2. anonymous

where u(t) has this form : |dw:1436021576568:dw|

3. anonymous

and I must calculate :$\int\limits_{0}^{5}y(t) dt$

4. anonymous

@oldrin.bataku never used that before but my question is: Does my diff eq has two solutions: y1(t) for t [0,2] y2(t) for t>2 ??

5. anonymous

$\int\limits_{0}^{5}y(t)dt=\int\limits_{0}^{2}y1(t)dt+\int\limits_{2}^{5}y2(t)dt$

6. anonymous

am I right ?

7. anonymous

there are distinct solutions, but you need ICs to 'glue' them together

8. anonymous

what's ICs ? Am I right with this distinct solutions ?

9. anonymous

Initial conditions do you mean right ?

10. anonymous

Can someone please guide me to all the steps needed(ICs,...) to help me understand this problem !

11. beginnersmind

"and I must calculate : ∫05y(t)dt" Maybe you don't need to solve the differential equation in general then

12. beginnersmind

If you express y(t) and integrate both sides from 0 to 5 you get a much simpler problem.

13. anonymous

can you be more specific please

14. anonymous

I mean how can I express something I don't know ? y(t) is the solution of that equation

15. anonymous

I forgot that the ICs are considered null.

16. beginnersmind

It's just an idea but I think it works |dw:1436022843809:dw|

17. beginnersmind

Assuming all derivates at 0 are zero, I get: |dw:1436023098647:dw|

18. beginnersmind

Where the integral with u(t) is known.

19. beginnersmind

Ok, not sure how to make progress from here. Maybe it doesn't work after all :(

20. anonymous

@ganeshie8 any idea ?

21. ganeshie8

is the order really 3 ?

22. anonymous

yup

23. anonymous

actually I don't need to solve this eq but rather I need to know if my presumption is right that the eq got two distinct solutins depending on u(t); am I right ?

24. ganeshie8

particular solution changes depending on u(t) but the homogeneous solution remains same

25. anonymous

well than I will reformulate the problem

26. anonymous

this eq needs to be solved using numerical analysis method RUNGE-Kutta in MatLab so I must transform this equation in a first degree equations

27. ganeshie8

try @dan815

28. anonymous

@dan815 are you familiar with matlab or numerical analysis ?

29. dan815

first order runge kutta = euler method right

30. anonymous

My question is if in my script of matlab do i need 2 functions: x1=Ax+5*b and x2=Ax+cos2t*b

31. dan815

and you have no initial values?

32. dan815

uh whats that for?

33. anonymous

Intial conditions are considered null

34. dan815

okay so first write a bunch of first order ODes

35. anonymous

That's for transforming the equation in a first order ODE

36. dan815

|dw:1436025643499:dw|

37. dan815

|dw:1436025758838:dw|

38. dan815

|dw:1436025814119:dw|

39. dan815

solve these in order

40. dan815

|dw:1436025883462:dw|

41. anonymous

Yeah right I think we should keep my notation as we are talking about vectors here: |dw:1436025828612:dw|

42. dan815

k thats looks fine

43. anonymous

the matrix A that I telled you behind looks like this 0 1 0 0 0 1 -2/3 -1/3 0

44. dan815

why are you putting it in a matrix

45. anonymous

x1=Ax+5*b and x2=Ax+cos2t*b |dw:1436026153233:dw|

46. anonymous

MATRIXlaboratory a.k.a MatLab

47. dan815

hmm let me think okay

48. dan815

if you want to solve it all in one matrix then, ud need it in the form like

49. anonymous

script: function x1=FCS(t,y) x1=A*x+b*5; end function x2=FCS(t,y) x2=A*x+b*cos(2t); end

50. dan815

|dw:1436026464161:dw|

51. dan815

|dw:1436026581332:dw|

52. dan815

im wondering if this is really possible in this case hmm

53. anonymous

dan I know that I'm just trying to understand my teacher method

54. dan815

what is his method?

55. anonymous

|dw:1436026645952:dw|

56. anonymous

than she makes a function : function xp=FCS(t,y) xp=A*x+b*u(t); end

57. dan815

so she got a new variable for x3

58. dan815

so that she doesnt have to worry about the extra vector

59. anonymous

then she does another script for the y function

60. dan815

|dw:1436026852588:dw|