## tmn50 2 years ago 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

1. Mashy

option 2

2. Mashy

since both are function of t!

3. abb0t

$F(y(t), t) = y \times G(t)$ ?

4. tmn50

yes

5. abb0t

$\frac{ ∂G }{ ∂t }$

6. tmn50

yes

7. Mashy

if both G and Y are function of t.. then you have to use the product rule!

8. tmn50

mashy our teacher used the first one in determining the solution of a differential equation of first order that's what makes me crazy

9. Mashy

no he mentioned its a function of time see the question!!

10. tmn50

y is a function of time

11. Mashy

Then Y must be independent of t... !!

12. abb0t

stop yelling @ me!! Ur hurting my feelings, bro :'(

13. Mashy

awww.. come here you !!

14. tmn50

-_-

15. Mashy

wow i get a medol and abbot gets none.. yay yay :P

16. tmn50

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

17. wio

Is it the partial derivative of $F(u, t)$Or of $F(y(t),t)$?

18. tmn50

the second one bro partial derevative with respect to t

19. wio

Well it was ambiguous, and $$F(u, t) \neq F(y(t),t)$$

20. tmn50

and so ?

21. Mashy

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 :-/

22. tmn50

-_- 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

23. Mashy

give me a differential equation!!

24. wio

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.

25. abb0t

well, that escalated quickly.

26. Mashy

lol :D

27. tmn50

M(y,t)dt+N(y,t)dy=0 where M=df/dt and N=df/dy

28. abb0t

Whoa, now we're doing ODE's?

29. Mashy

thats called as EXACT FORM right?

30. abb0t

Correct, Mashy :)

31. tmn50

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

32. Mashy

well then in that.. case.. i have forgetting how to do it :D

33. abb0t

This is escalating too damn quickly.

34. tmn50

it's like i have holes in mathematics so when i advance i fall into some of them

35. Mashy

holes in mathematics.. lol funny :D

36. wio

Can you give us $$M, N$$?

37. Mashy

he already mentioned.. df/dy and df/dt!

38. abb0t

Well, you want to find the PD for either M or N first. I think it's ∂M/∂x and ∂N/∂y ?

39. tmn50

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)

40. Mashy

wow i did this 4 years back!! ..

41. Mashy

so i don't remember much :-/

42. tmn50

43. abb0t

Well, you have to check that they are exact first for this to work.

44. abb0t

Otherwise, you are wasting time trying to do furhter work than is necessary.

45. wio

$\begin{array}{rcl} M(y,t)dt+N(y,t)dy &=& 0 \\ M(y,t)dt &=& -N(y,t)dy \end{array}$ I would try integrating $$M$$ with respect to $$t$$ and then differentiating with respect to $$y$$.

46. tmn50

wait can i post a picture ?

47. tmn50

yup i can wait

48. tmn50

49. Mashy

really?!? of yourself?? we are in the middle of math here!

50. tmn50

here check tht

51. tmn50

i'm too handsome :p

52. Mashy

so i have heard :P

53. Mashy

i mean .. i did.. just now :P.. from you!!

54. tmn50

so any idea about what i posted?

55. abb0t

What it looks like you're trying to do in that step is find a integrating factor to make the solution exact?

56. tmn50

yup

57. tmn50

wait wait wait we found the integrating factor we're in the middle of finding F

58. tmn50

see where's the arrow pointing

59. abb0t

I'm not quite sure what you did there, I'm used to doing it a different method..

60. tmn50

tht's the teacher's doing not me :3

61. tmn50

oh well i'm off now i'll check again after half an hour or so thanks ppl

62. tmn50

i'm back people any news,