tmn50
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
Delete
Share
This Question is Closed
Mashy
Best Response
You've already chosen the best response.
1
option 2
Mashy
Best Response
You've already chosen the best response.
1
since both are function of t!
abb0t
Best Response
You've already chosen the best response.
1
\[F(y(t), t) = y \times G(t)\] ?
tmn50
Best Response
You've already chosen the best response.
0
yes
abb0t
Best Response
You've already chosen the best response.
1
\[\frac{ ∂G }{ ∂t }\]
tmn50
Best Response
You've already chosen the best response.
0
yes
Mashy
Best Response
You've already chosen the best response.
1
if both G and Y are function of t.. then you have to use the product rule!
tmn50
Best Response
You've already chosen the best response.
0
mashy our teacher used the first one in determining the solution of a differential equation of first order that's what makes me crazy
Mashy
Best Response
You've already chosen the best response.
1
no he mentioned its a function of time see the question!!
tmn50
Best Response
You've already chosen the best response.
0
y is a function of time
Mashy
Best Response
You've already chosen the best response.
1
Then Y must be independent of t... !!
abb0t
Best Response
You've already chosen the best response.
1
stop yelling @ me!! Ur hurting my feelings, bro :'(
Mashy
Best Response
You've already chosen the best response.
1
awww.. come here you !!
tmn50
Best Response
You've already chosen the best response.
0
-_-
Mashy
Best Response
You've already chosen the best response.
1
wow i get a medol and abbot gets none.. yay yay :P
tmn50
Best Response
You've already chosen the best response.
0
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
wio
Best Response
You've already chosen the best response.
1
Is it the partial derivative of \[
F(u, t)
\]Or of \[
F(y(t),t)
\]?
tmn50
Best Response
You've already chosen the best response.
0
the second one bro partial derevative with respect to t
wio
Best Response
You've already chosen the best response.
1
Well it was ambiguous, and \(F(u, t) \neq F(y(t),t)\)
tmn50
Best Response
You've already chosen the best response.
0
and so ?
Mashy
Best Response
You've already chosen the best response.
1
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 :-/
tmn50
Best Response
You'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
Best Response
You've already chosen the best response.
1
give me a differential equation!!
wio
Best Response
You've already chosen the best response.
1
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.
abb0t
Best Response
You've already chosen the best response.
1
well, that escalated quickly.
Mashy
Best Response
You've already chosen the best response.
1
lol :D
tmn50
Best Response
You've already chosen the best response.
0
M(y,t)dt+N(y,t)dy=0 where M=df/dt and N=df/dy
abb0t
Best Response
You've already chosen the best response.
1
Whoa, now we're doing ODE's?
Mashy
Best Response
You've already chosen the best response.
1
thats called as EXACT FORM right?
abb0t
Best Response
You've already chosen the best response.
1
Correct, Mashy :)
tmn50
Best Response
You've already chosen the best response.
0
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
Mashy
Best Response
You've already chosen the best response.
1
well then in that.. case.. i have forgetting how to do it :D
abb0t
Best Response
You've already chosen the best response.
1
This is escalating too damn quickly.
tmn50
Best Response
You've already chosen the best response.
0
it's like i have holes in mathematics so when i advance i fall into some of them
Mashy
Best Response
You've already chosen the best response.
1
holes in mathematics.. lol funny :D
wio
Best Response
You've already chosen the best response.
1
Can you give us \(M, N\)?
Mashy
Best Response
You've already chosen the best response.
1
he already mentioned.. df/dy and df/dt!
abb0t
Best Response
You've already chosen the best response.
1
Well, you want to find the PD for either M or N first. I think it's ∂M/∂x and ∂N/∂y ?
tmn50
Best Response
You've already chosen the best response.
0
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)
Mashy
Best Response
You've already chosen the best response.
1
wow i did this 4 years back!! ..
Mashy
Best Response
You've already chosen the best response.
1
so i don't remember much :-/
tmn50
Best Response
You've already chosen the best response.
0
sadly
abb0t
Best Response
You've already chosen the best response.
1
Well, you have to check that they are exact first for this to work.
abb0t
Best Response
You've already chosen the best response.
1
Otherwise, you are wasting time trying to do furhter work than is necessary.
wio
Best Response
You'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
Best Response
You've already chosen the best response.
0
wait
can i post a picture ?
tmn50
Best Response
You've already chosen the best response.
0
yup i can wait
tmn50
Best Response
You've already chosen the best response.
0
Mashy
Best Response
You've already chosen the best response.
1
really?!? of yourself?? we are in the middle of math here!
tmn50
Best Response
You've already chosen the best response.
0
here check tht
tmn50
Best Response
You've already chosen the best response.
0
i'm too handsome :p
Mashy
Best Response
You've already chosen the best response.
1
so i have heard :P
Mashy
Best Response
You've already chosen the best response.
1
i mean .. i did.. just now :P.. from you!!
tmn50
Best Response
You've already chosen the best response.
0
so any idea about what i posted?
abb0t
Best Response
You've already chosen the best response.
1
What it looks like you're trying to do in that step is find a integrating factor to make the solution exact?
tmn50
Best Response
You've already chosen the best response.
0
yup
tmn50
Best Response
You've already chosen the best response.
0
wait wait wait we found the integrating factor we're in the middle of finding F
tmn50
Best Response
You've already chosen the best response.
0
see where's the arrow pointing
abb0t
Best Response
You've already chosen the best response.
1
I'm not quite sure what you did there, I'm used to doing it a different method..
tmn50
Best Response
You've already chosen the best response.
0
tht's the teacher's doing not me :3
tmn50
Best Response
You've already chosen the best response.
0
oh well i'm off now i'll check again after half an hour or so thanks ppl
tmn50
Best Response
You've already chosen the best response.
0
i'm back people any news,