Mixing
Hard partial differential equation leading to separation of variable - help
$begingroup$
Ok i need some help, i have been trying to do this for a few days and i cant do it. Any help would be appreciated.
So we are given equation 1 (i think you have to click on the link to see the equation) and the end goal is to solve for u(r,t).
equation 1
but this is not possible in this format, so we decompose it using
u(r,t) = v(r,t) + w(r)
we obtain the equation shown below:
equation 2
this gives us a simple way to solve for w(r).
now the part i am stuck at, is it says to use
v(r,t) = u(r,t) - w(r)
and equation 1 or 2 to formulate a pde that is homogeneous to solve for v(r,t)
after this we can use
y(r,t) = v(r,t)*r
to obtain equation 3 shown in below
equation 3
someone pls help me formulate the pde for v(r,t) that eventually leads to equation 3.
derivatives pde partial-derivative
asked Jan 29 at 13:02
ElecLearnElecLearn
11
$endgroup$
add a comment |
$begingroup$
Ok i need some help, i have been trying to do this for a few days and i cant do it. Any help would be appreciated.
So we are given equation 1 (i think you have to click on the link to see the equation) and the end goal is to solve for u(r,t).
equation 1
but this is not possible in this format, so we decompose it using
u(r,t) = v(r,t) + w(r)
we obtain the equation shown below:
equation 2
this gives us a simple way to solve for w(r).
now the part i am stuck at, is it says to use
v(r,t) = u(r,t) - w(r)
and equation 1 or 2 to formulate a pde that is homogeneous to solve for v(r,t)
after this we can use
y(r,t) = v(r,t)*r
to obtain equation 3 shown in below
equation 3
someone pls help me formulate the pde for v(r,t) that eventually leads to equation 3.
derivatives pde partial-derivative
asked Jan 29 at 13:02
ElecLearnElecLearn
11
$endgroup$
$begingroup$
Hi! Welcome to MSE. In order to allow people to be able to read your question conveniently, please use mathjax to typeset the equations - here's a guide. Also please include in the question exactly what you've tried to do, and how you are stuck. This helps people understand where you are w.r.t. the question, and what kind of answers would be helpful to you.
$endgroup$
– stochasticboy321
Jan 29 at 14:52
add a comment |
$begingroup$
Ok i need some help, i have been trying to do this for a few days and i cant do it. Any help would be appreciated.
So we are given equation 1 (i think you have to click on the link to see the equation) and the end goal is to solve for u(r,t).
equation 1
but this is not possible in this format, so we decompose it using
u(r,t) = v(r,t) + w(r)
we obtain the equation shown below:
equation 2
this gives us a simple way to solve for w(r).
now the part i am stuck at, is it says to use
v(r,t) = u(r,t) - w(r)
and equation 1 or 2 to formulate a pde that is homogeneous to solve for v(r,t)
after this we can use
y(r,t) = v(r,t)*r
to obtain equation 3 shown in below
equation 3
someone pls help me formulate the pde for v(r,t) that eventually leads to equation 3.
derivatives pde partial-derivative
asked Jan 29 at 13:02
ElecLearnElecLearn
11
$endgroup$
Ok i need some help, i have been trying to do this for a few days and i cant do it. Any help would be appreciated.
So we are given equation 1 (i think you have to click on the link to see the equation) and the end goal is to solve for u(r,t).
equation 1
but this is not possible in this format, so we decompose it using
u(r,t) = v(r,t) + w(r)
we obtain the equation shown below:
equation 2
this gives us a simple way to solve for w(r).
now the part i am stuck at, is it says to use
v(r,t) = u(r,t) - w(r)
and equation 1 or 2 to formulate a pde that is homogeneous to solve for v(r,t)
after this we can use
y(r,t) = v(r,t)*r
to obtain equation 3 shown in below
equation 3
someone pls help me formulate the pde for v(r,t) that eventually leads to equation 3.
derivatives pde partial-derivative
derivatives pde partial-derivative
asked Jan 29 at 13:02
ElecLearnElecLearn
11
asked Jan 29 at 13:02
ElecLearnElecLearn
11
asked Jan 29 at 13:02
ElecLearnElecLearn
11
asked Jan 29 at 13:02
ElecLearnElecLearn
11
asked Jan 29 at 13:02
ElecLearnElecLearn
11
11
$begingroup$
Hi! Welcome to MSE. In order to allow people to be able to read your question conveniently, please use mathjax to typeset the equations - here's a guide. Also please include in the question exactly what you've tried to do, and how you are stuck. This helps people understand where you are w.r.t. the question, and what kind of answers would be helpful to you.
$endgroup$
– stochasticboy321
Jan 29 at 14:52
add a comment |
$begingroup$
Hi! Welcome to MSE. In order to allow people to be able to read your question conveniently, please use mathjax to typeset the equations - here's a guide. Also please include in the question exactly what you've tried to do, and how you are stuck. This helps people understand where you are w.r.t. the question, and what kind of answers would be helpful to you.
$endgroup$
– stochasticboy321
Jan 29 at 14:52
$begingroup$
Hi! Welcome to MSE. In order to allow people to be able to read your question conveniently, please use mathjax to typeset the equations - here's a guide. Also please include in the question exactly what you've tried to do, and how you are stuck. This helps people understand where you are w.r.t. the question, and what kind of answers would be helpful to you.
$endgroup$
– stochasticboy321
Jan 29 at 14:52
$begingroup$
Hi! Welcome to MSE. In order to allow people to be able to read your question conveniently, please use mathjax to typeset the equations - here's a guide. Also please include in the question exactly what you've tried to do, and how you are stuck. This helps people understand where you are w.r.t. the question, and what kind of answers would be helpful to you.
$endgroup$
– stochasticboy321
Jan 29 at 14:52
add a comment |
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$begingroup$
Hi! Welcome to MSE. In order to allow people to be able to read your question conveniently, please use mathjax to typeset the equations - here's a guide. Also please include in the question exactly what you've tried to do, and how you are stuck. This helps people understand where you are w.r.t. the question, and what kind of answers would be helpful to you.
$endgroup$
– stochasticboy321
Jan 29 at 14:52