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 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
 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

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Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1since both are function of t!

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1\[F(y(t), t) = y \times G(t)\] ?

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1if both G and Y are function of t.. then you have to use the product rule!

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0mashy our teacher used the first one in determining the solution of a differential equation of first order that's what makes me crazy

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1no he mentioned its a function of time see the question!!

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1Then Y must be independent of t... !!

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1stop yelling @ me!! Ur hurting my feelings, bro :'(

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1wow i get a medol and abbot gets none.. yay yay :P

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0who 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

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Is it the partial derivative of \[ F(u, t) \]Or of \[ F(y(t),t) \]?

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0the second one bro partial derevative with respect to t

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Well it was ambiguous, and \(F(u, t) \neq F(y(t),t)\)

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1if 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 :/

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0_ 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

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1give me a differential equation!!

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Like @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.

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1well, that escalated quickly.

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0M(y,t)dt+N(y,t)dy=0 where M=df/dt and N=df/dy

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1Whoa, now we're doing ODE's?

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1thats called as EXACT FORM right?

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0wio 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

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1well then in that.. case.. i have forgetting how to do it :D

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1This is escalating too damn quickly.

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0it's like i have holes in mathematics so when i advance i fall into some of them

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1holes in mathematics.. lol funny :D

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1he already mentioned.. df/dy and df/dt!

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1Well, you want to find the PD for either M or N first. I think it's ∂M/∂x and ∂N/∂y ?

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0it 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)

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1wow i did this 4 years back!! ..

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1so i don't remember much :/

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1Well, you have to check that they are exact first for this to work.

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1Otherwise, you are wasting time trying to do furhter work than is necessary.

wio
 2 years ago
Best ResponseYou've already chosen the best response.1\[ \begin{array}{rcl} M(y,t)dt+N(y,t)dy &=& 0 \\ M(y,t)dt &=& N(y,t)dy \end{array} \] I would try integrating \(M\) with respect to \(t\) and then differentiating with respect to \(y\).

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0wait can i post a picture ?

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1really?!? of yourself?? we are in the middle of math here!

Mashy
 2 years ago
Best ResponseYou've already chosen the best response.1i mean .. i did.. just now :P.. from you!!

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0so any idea about what i posted?

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1What it looks like you're trying to do in that step is find a integrating factor to make the solution exact?

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0wait wait wait we found the integrating factor we're in the middle of finding F

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0see where's the arrow pointing

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1I'm not quite sure what you did there, I'm used to doing it a different method..

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0tht's the teacher's doing not me :3

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0oh well i'm off now i'll check again after half an hour or so thanks ppl

tmn50
 2 years ago
Best ResponseYou've already chosen the best response.0i'm back people any news,
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