Mixing
2015 gate question from partial differential equation and based on laplace equation
$begingroup$
I dont know about such functions which satisfy these conditions given in question
Let $$Omega={{(x,y)in R^2 | x^2+y^2lt1}}$$ be the open unit disk in $R^2$ with boundary $partialOmega$. If $u(x,y)$ is the solution of the Dirchlet Problem:
$$u_{x x}+u_{y y} =0 spacespace in spaceOmega$$
$$ u(x,y)=1-2y^2space in space partialOmega$$
Then $u(frac{1}{2},0)$ is equal to
$(a) -1$ $space$ $(b)-frac{1}{4}$ $space$ $(c) frac{1}{4}$ $space$ $(d)1$
Can you help me out ?
ordinary-differential-equations
edited Jan 26 at 12:26
SNEHIL SANYAL
654110
asked Jan 26 at 11:48
sweety tarikasweety tarika
255
$endgroup$
add a comment |
$begingroup$
I dont know about such functions which satisfy these conditions given in question
Let $$Omega={{(x,y)in R^2 | x^2+y^2lt1}}$$ be the open unit disk in $R^2$ with boundary $partialOmega$. If $u(x,y)$ is the solution of the Dirchlet Problem:
$$u_{x x}+u_{y y} =0 spacespace in spaceOmega$$
$$ u(x,y)=1-2y^2space in space partialOmega$$
Then $u(frac{1}{2},0)$ is equal to
$(a) -1$ $space$ $(b)-frac{1}{4}$ $space$ $(c) frac{1}{4}$ $space$ $(d)1$
Can you help me out ?
ordinary-differential-equations
edited Jan 26 at 12:26
SNEHIL SANYAL
654110
asked Jan 26 at 11:48
sweety tarikasweety tarika
255
$endgroup$
$begingroup$
DId you try anything at all ? It's hard to know how to help you consturctively without having any context whatsoever.
$endgroup$
– J.F
Jan 26 at 11:55
$begingroup$
x²⁻y² example dont strike in my mind, i was thinking about log⁽x²⁺y²⁾, y/x²⁺y² functions only
$endgroup$
– sweety tarika
Jan 26 at 15:16
add a comment |
$begingroup$
I dont know about such functions which satisfy these conditions given in question
Let $$Omega={{(x,y)in R^2 | x^2+y^2lt1}}$$ be the open unit disk in $R^2$ with boundary $partialOmega$. If $u(x,y)$ is the solution of the Dirchlet Problem:
$$u_{x x}+u_{y y} =0 spacespace in spaceOmega$$
$$ u(x,y)=1-2y^2space in space partialOmega$$
Then $u(frac{1}{2},0)$ is equal to
$(a) -1$ $space$ $(b)-frac{1}{4}$ $space$ $(c) frac{1}{4}$ $space$ $(d)1$
Can you help me out ?
ordinary-differential-equations
edited Jan 26 at 12:26
SNEHIL SANYAL
654110
asked Jan 26 at 11:48
sweety tarikasweety tarika
255
$endgroup$
I dont know about such functions which satisfy these conditions given in question
Let $$Omega={{(x,y)in R^2 | x^2+y^2lt1}}$$ be the open unit disk in $R^2$ with boundary $partialOmega$. If $u(x,y)$ is the solution of the Dirchlet Problem:
$$u_{x x}+u_{y y} =0 spacespace in spaceOmega$$
$$ u(x,y)=1-2y^2space in space partialOmega$$
Then $u(frac{1}{2},0)$ is equal to
$(a) -1$ $space$ $(b)-frac{1}{4}$ $space$ $(c) frac{1}{4}$ $space$ $(d)1$
Can you help me out ?
ordinary-differential-equations
ordinary-differential-equations
edited Jan 26 at 12:26
SNEHIL SANYAL
654110
asked Jan 26 at 11:48
sweety tarikasweety tarika
255
edited Jan 26 at 12:26
SNEHIL SANYAL
654110
asked Jan 26 at 11:48
sweety tarikasweety tarika
255
edited Jan 26 at 12:26
SNEHIL SANYAL
654110
edited Jan 26 at 12:26
SNEHIL SANYAL
654110
edited Jan 26 at 12:26
SNEHIL SANYAL
654110
654110
asked Jan 26 at 11:48
sweety tarikasweety tarika
255
asked Jan 26 at 11:48
sweety tarikasweety tarika
255
asked Jan 26 at 11:48
sweety tarikasweety tarika
255
255
$begingroup$
DId you try anything at all ? It's hard to know how to help you consturctively without having any context whatsoever.
$endgroup$
– J.F
Jan 26 at 11:55
$begingroup$
x²⁻y² example dont strike in my mind, i was thinking about log⁽x²⁺y²⁾, y/x²⁺y² functions only
$endgroup$
– sweety tarika
Jan 26 at 15:16
add a comment |
$begingroup$
DId you try anything at all ? It's hard to know how to help you consturctively without having any context whatsoever.
$endgroup$
– J.F
Jan 26 at 11:55
$begingroup$
x²⁻y² example dont strike in my mind, i was thinking about log⁽x²⁺y²⁾, y/x²⁺y² functions only
$endgroup$
– sweety tarika
Jan 26 at 15:16
$begingroup$
DId you try anything at all ? It's hard to know how to help you consturctively without having any context whatsoever.
$endgroup$
– J.F
Jan 26 at 11:55
$begingroup$
DId you try anything at all ? It's hard to know how to help you consturctively without having any context whatsoever.
$endgroup$
– J.F
Jan 26 at 11:55
$begingroup$
x²⁻y² example dont strike in my mind, i was thinking about log⁽x²⁺y²⁾, y/x²⁺y² functions only
$endgroup$
– sweety tarika
Jan 26 at 15:16
$begingroup$
x²⁻y² example dont strike in my mind, i was thinking about log⁽x²⁺y²⁾, y/x²⁺y² functions only
$endgroup$
– sweety tarika
Jan 26 at 15:16
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
see for example: https://nptel.ac.in/courses/111103021/33.pdf
In polar coordinates solution is
$$u=r^2cos(2theta)$$
In Cartesian coordinates solution is
$$u(x,y)=x^2-y^2$$
Then
$$u(frac12,0)=frac14.$$
answered Jan 26 at 12:31
Aleksas DomarkasAleksas Domarkas
1,54817
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
see for example: https://nptel.ac.in/courses/111103021/33.pdf
In polar coordinates solution is
$$u=r^2cos(2theta)$$
In Cartesian coordinates solution is
$$u(x,y)=x^2-y^2$$
Then
$$u(frac12,0)=frac14.$$
answered Jan 26 at 12:31
Aleksas DomarkasAleksas Domarkas
1,54817
$endgroup$
add a comment |
$begingroup$
see for example: https://nptel.ac.in/courses/111103021/33.pdf
In polar coordinates solution is
$$u=r^2cos(2theta)$$
In Cartesian coordinates solution is
$$u(x,y)=x^2-y^2$$
Then
$$u(frac12,0)=frac14.$$
answered Jan 26 at 12:31
Aleksas DomarkasAleksas Domarkas
1,54817
$endgroup$
add a comment |
$begingroup$
see for example: https://nptel.ac.in/courses/111103021/33.pdf
In polar coordinates solution is
$$u=r^2cos(2theta)$$
In Cartesian coordinates solution is
$$u(x,y)=x^2-y^2$$
Then
$$u(frac12,0)=frac14.$$
answered Jan 26 at 12:31
Aleksas DomarkasAleksas Domarkas
1,54817
$endgroup$
see for example: https://nptel.ac.in/courses/111103021/33.pdf
In polar coordinates solution is
$$u=r^2cos(2theta)$$
In Cartesian coordinates solution is
$$u(x,y)=x^2-y^2$$
Then
$$u(frac12,0)=frac14.$$
answered Jan 26 at 12:31
Aleksas DomarkasAleksas Domarkas
1,54817
answered Jan 26 at 12:31
Aleksas DomarkasAleksas Domarkas
1,54817
answered Jan 26 at 12:31
Aleksas DomarkasAleksas Domarkas
1,54817
answered Jan 26 at 12:31
Aleksas DomarkasAleksas Domarkas
1,54817
1,54817
add a comment |
add a comment |
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$begingroup$
DId you try anything at all ? It's hard to know how to help you consturctively without having any context whatsoever.
$endgroup$
– J.F
Jan 26 at 11:55
$begingroup$
x²⁻y² example dont strike in my mind, i was thinking about log⁽x²⁺y²⁾, y/x²⁺y² functions only
$endgroup$
– sweety tarika
Jan 26 at 15:16