## 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

1. Mashy Group Title

option 2

2. Mashy Group Title

since both are function of t!

3. abb0t Group Title

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

4. tmn50 Group Title

yes

5. abb0t Group Title

$\frac{ ∂G }{ ∂t }$

6. tmn50 Group Title

yes

7. Mashy Group Title

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

8. tmn50 Group Title

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 Group Title

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

10. tmn50 Group Title

y is a function of time

11. Mashy Group Title

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

12. abb0t Group Title

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

13. Mashy Group Title

awww.. come here you !!

14. tmn50 Group Title

-_-

15. Mashy Group Title

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

16. tmn50 Group Title

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 Group Title

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

18. tmn50 Group Title

the second one bro partial derevative with respect to t

19. wio Group Title

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

20. tmn50 Group Title

and so ?

21. Mashy Group Title

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 Group Title

-_- 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 Group Title

give me a differential equation!!

24. wio Group Title

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 Group Title

well, that escalated quickly.

26. Mashy Group Title

lol :D

27. tmn50 Group Title

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

28. abb0t Group Title

Whoa, now we're doing ODE's?

29. Mashy Group Title

thats called as EXACT FORM right?

30. abb0t Group Title

Correct, Mashy :)

31. tmn50 Group Title

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 Group Title

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

33. abb0t Group Title

This is escalating too damn quickly.

34. tmn50 Group Title

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

35. Mashy Group Title

holes in mathematics.. lol funny :D

36. wio Group Title

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

37. Mashy Group Title

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

38. abb0t Group Title

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

39. tmn50 Group Title

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 Group Title

wow i did this 4 years back!! ..

41. Mashy Group Title

so i don't remember much :-/

42. tmn50 Group Title

43. abb0t Group Title

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

44. abb0t Group Title

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

45. wio Group Title

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

46. tmn50 Group Title

wait can i post a picture ?

47. tmn50 Group Title

yup i can wait

48. tmn50 Group Title

49. Mashy Group Title

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

50. tmn50 Group Title

here check tht

51. tmn50 Group Title

i'm too handsome :p

52. Mashy Group Title

so i have heard :P

53. Mashy Group Title

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

54. tmn50 Group Title

so any idea about what i posted?

55. abb0t Group Title

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

56. tmn50 Group Title

yup

57. tmn50 Group Title

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

58. tmn50 Group Title

see where's the arrow pointing

59. abb0t Group Title

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

60. tmn50 Group Title

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

61. tmn50 Group Title

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

62. tmn50 Group Title

i'm back people any news,