Find the solution of the Clairaut equation
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How do you find the solution of the Clairaut equation
$$u = xu_{x} + yu_{y} + sqrt{1 + u^2_{x} + u^ 2_{y}}$$
with initial data
$$ x(0, s) = acos(s)$$$$ y(0, s) =acos(s) $$$$u(0, s) = 0,$$
where α is a constant
such that α > 1.
pde wave-equation
asked Nov 17 at 21:29
Tim Jones
1019
add a comment |
up vote
0
down vote
favorite
How do you find the solution of the Clairaut equation
$$u = xu_{x} + yu_{y} + sqrt{1 + u^2_{x} + u^ 2_{y}}$$
with initial data
$$ x(0, s) = acos(s)$$$$ y(0, s) =acos(s) $$$$u(0, s) = 0,$$
where α is a constant
such that α > 1.
pde wave-equation
asked Nov 17 at 21:29
Tim Jones
1019
It seems the initial data is not consistent with your pde. What's the relation between $x$ and $y$ with $s$. Are we supposed to use the the method of characteristics?
– minimax
Nov 17 at 22:03
Have you tried to differentiate it with wrt $x$ and then wrt $y$?
– minimax
Nov 17 at 22:07
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How do you find the solution of the Clairaut equation
$$u = xu_{x} + yu_{y} + sqrt{1 + u^2_{x} + u^ 2_{y}}$$
with initial data
$$ x(0, s) = acos(s)$$$$ y(0, s) =acos(s) $$$$u(0, s) = 0,$$
where α is a constant
such that α > 1.
pde wave-equation
asked Nov 17 at 21:29
Tim Jones
1019
How do you find the solution of the Clairaut equation
$$u = xu_{x} + yu_{y} + sqrt{1 + u^2_{x} + u^ 2_{y}}$$
with initial data
$$ x(0, s) = acos(s)$$$$ y(0, s) =acos(s) $$$$u(0, s) = 0,$$
where α is a constant
such that α > 1.
pde wave-equation
pde wave-equation
asked Nov 17 at 21:29
Tim Jones
1019
asked Nov 17 at 21:29
Tim Jones
1019
edited Nov 20 at 0:20
asked Nov 17 at 21:29
Tim Jones
1019
asked Nov 17 at 21:29
Tim Jones
1019
asked Nov 17 at 21:29
Tim Jones
1019
1019
It seems the initial data is not consistent with your pde. What's the relation between $x$ and $y$ with $s$. Are we supposed to use the the method of characteristics?
– minimax
Nov 17 at 22:03
Have you tried to differentiate it with wrt $x$ and then wrt $y$?
– minimax
Nov 17 at 22:07
add a comment |
It seems the initial data is not consistent with your pde. What's the relation between $x$ and $y$ with $s$. Are we supposed to use the the method of characteristics?
– minimax
Nov 17 at 22:03
Have you tried to differentiate it with wrt $x$ and then wrt $y$?
– minimax
Nov 17 at 22:07
It seems the initial data is not consistent with your pde. What's the relation between $x$ and $y$ with $s$. Are we supposed to use the the method of characteristics?
– minimax
Nov 17 at 22:03
It seems the initial data is not consistent with your pde. What's the relation between $x$ and $y$ with $s$. Are we supposed to use the the method of characteristics?
– minimax
Nov 17 at 22:03
Have you tried to differentiate it with wrt $x$ and then wrt $y$?
– minimax
Nov 17 at 22:07
Have you tried to differentiate it with wrt $x$ and then wrt $y$?
– minimax
Nov 17 at 22:07
add a comment |
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It seems the initial data is not consistent with your pde. What's the relation between $x$ and $y$ with $s$. Are we supposed to use the the method of characteristics?
– minimax
Nov 17 at 22:03
Have you tried to differentiate it with wrt $x$ and then wrt $y$?
– minimax
Nov 17 at 22:07