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tmn50 Group Title

let's say we have a function F(y(t),t)=y*G(t) the partial derevative of F with respect to t is y*dG/dt or dy/dt*G+dG/dt*y I would really apreciate an explanation

  • one year ago
  • one year ago

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  1. Mashy Group Title
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    option 2

    • one year ago
  2. Mashy Group Title
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    since both are function of t!

    • one year ago
  3. abb0t Group Title
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    \[F(y(t), t) = y \times G(t)\] ?

    • one year ago
  4. tmn50 Group Title
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    yes

    • one year ago
  5. abb0t Group Title
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    \[\frac{ ∂G }{ ∂t }\]

    • one year ago
  6. tmn50 Group Title
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    yes

    • one year ago
  7. Mashy Group Title
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    if both G and Y are function of t.. then you have to use the product rule!

    • one year ago
  8. tmn50 Group Title
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    mashy our teacher used the first one in determining the solution of a differential equation of first order that's what makes me crazy

    • one year ago
  9. Mashy Group Title
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    no he mentioned its a function of time see the question!!

    • one year ago
  10. tmn50 Group Title
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    y is a function of time

    • one year ago
  11. Mashy Group Title
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    Then Y must be independent of t... !!

    • one year ago
  12. abb0t Group Title
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    stop yelling @ me!! Ur hurting my feelings, bro :'(

    • one year ago
  13. Mashy Group Title
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    awww.. come here you !!

    • one year ago
  14. tmn50 Group Title
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    -_-

    • one year ago
  15. Mashy Group Title
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    wow i get a medol and abbot gets none.. yay yay :P

    • one year ago
  16. tmn50 Group Title
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    who the hell gave u a medal i think your answer is wrong man here we're talking about partial derevative which is diffrent from derevating everything with respect to t

    • one year ago
  17. wio Group Title
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    Is it the partial derivative of \[ F(u, t) \]Or of \[ F(y(t),t) \]?

    • one year ago
  18. tmn50 Group Title
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    the second one bro partial derevative with respect to t

    • one year ago
  19. wio Group Title
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    Well it was ambiguous, and \(F(u, t) \neq F(y(t),t)\)

    • one year ago
  20. tmn50 Group Title
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    and so ?

    • one year ago
  21. Mashy Group Title
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    if both functions are time dependent.. then really there is no difference between partial and normal derivatives.. HELL why would you even DO a partial derivative doesn't even make any sense :-/

    • one year ago
  22. tmn50 Group Title
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    -_- it makes sense when u'r solving a diferential equation of first order first you find F(y,t) then you derevative partially with respect to y or t and force it to be equal to the equation you have left so yeh u need a partial derevative

    • one year ago
  23. Mashy Group Title
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    give me a differential equation!!

    • one year ago
  24. wio Group Title
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    Like @Mashy is saying, \(F(y(t),t)\) doesn't have a partial derivative because it is not a multiple variable function. It's the OUTPUT of \(F(u, t)\) which happens to be a single variable function.

    • one year ago
  25. abb0t Group Title
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    well, that escalated quickly.

    • one year ago
  26. Mashy Group Title
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    lol :D

    • one year ago
  27. tmn50 Group Title
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    M(y,t)dt+N(y,t)dy=0 where M=df/dt and N=df/dy

    • one year ago
  28. abb0t Group Title
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    Whoa, now we're doing ODE's?

    • one year ago
  29. Mashy Group Title
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    thats called as EXACT FORM right?

    • one year ago
  30. abb0t Group Title
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    Correct, Mashy :)

    • one year ago
  31. tmn50 Group Title
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    wio i didnt catch up with what you said i mean here we got 2 variable well not two variables y is a function of time and hell

    • one year ago
  32. Mashy Group Title
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    well then in that.. case.. i have forgetting how to do it :D

    • one year ago
  33. abb0t Group Title
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    This is escalating too damn quickly.

    • one year ago
  34. tmn50 Group Title
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    it's like i have holes in mathematics so when i advance i fall into some of them

    • one year ago
  35. Mashy Group Title
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    holes in mathematics.. lol funny :D

    • one year ago
  36. wio Group Title
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    Can you give us \(M, N\)?

    • one year ago
  37. Mashy Group Title
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    he already mentioned.. df/dy and df/dt!

    • one year ago
  38. abb0t Group Title
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    Well, you want to find the PD for either M or N first. I think it's ∂M/∂x and ∂N/∂y ?

    • one year ago
  39. tmn50 Group Title
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    it doesn't matter what M and N are the only restriction is that M and N are the partial derevatives of a certain function F(y,t)

    • one year ago
  40. Mashy Group Title
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    wow i did this 4 years back!! ..

    • one year ago
  41. Mashy Group Title
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    so i don't remember much :-/

    • one year ago
  42. tmn50 Group Title
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    sadly

    • one year ago
  43. abb0t Group Title
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    Well, you have to check that they are exact first for this to work.

    • one year ago
  44. abb0t Group Title
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    Otherwise, you are wasting time trying to do furhter work than is necessary.

    • one year ago
  45. wio Group Title
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    \[ \begin{array}{rcl} M(y,t)dt+N(y,t)dy &=& 0 \\ M(y,t)dt &=& -N(y,t)dy \end{array} \] I would try integrating \(M\) with respect to \(t\) and then differentiating with respect to \(y\).

    • one year ago
  46. tmn50 Group Title
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    wait can i post a picture ?

    • one year ago
  47. tmn50 Group Title
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    yup i can wait

    • one year ago
  48. tmn50 Group Title
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    • one year ago
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  49. Mashy Group Title
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    really?!? of yourself?? we are in the middle of math here!

    • one year ago
  50. tmn50 Group Title
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    here check tht

    • one year ago
  51. tmn50 Group Title
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    i'm too handsome :p

    • one year ago
  52. Mashy Group Title
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    so i have heard :P

    • one year ago
  53. Mashy Group Title
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    i mean .. i did.. just now :P.. from you!!

    • one year ago
  54. tmn50 Group Title
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    so any idea about what i posted?

    • one year ago
  55. abb0t Group Title
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    What it looks like you're trying to do in that step is find a integrating factor to make the solution exact?

    • one year ago
  56. tmn50 Group Title
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    yup

    • one year ago
  57. tmn50 Group Title
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    wait wait wait we found the integrating factor we're in the middle of finding F

    • one year ago
  58. tmn50 Group Title
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    see where's the arrow pointing

    • one year ago
  59. abb0t Group Title
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    I'm not quite sure what you did there, I'm used to doing it a different method..

    • one year ago
  60. tmn50 Group Title
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    tht's the teacher's doing not me :3

    • one year ago
  61. tmn50 Group Title
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    oh well i'm off now i'll check again after half an hour or so thanks ppl

    • one year ago
  62. tmn50 Group Title
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    i'm back people any news,

    • one year ago
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