Help with “partial differential equation” definition
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From wikipedia: "PDE is a differential equation that contains beforehand unknown multivariable functions and their partial derivatives".
My dubt is: suppose you have the following variable
$u =u(x_1, x_2)$
where $x_1$ and $x_2$ are independent variables
and a particular physical problem that is modeled with one the following equations:
1) $frac{du}{dx_1}=5$
2) $frac{du}{dx_1}=5*x_1$
3) $frac{du}{dx_1}=5*x_2$
Can this equations be considered as PDE since in those appears only the derivative with respect a one of the dependent variables?
terminology
asked Jan 18 at 13:45
user2235427user2235427
1083
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add a comment |
$begingroup$
From wikipedia: "PDE is a differential equation that contains beforehand unknown multivariable functions and their partial derivatives".
My dubt is: suppose you have the following variable
$u =u(x_1, x_2)$
where $x_1$ and $x_2$ are independent variables
and a particular physical problem that is modeled with one the following equations:
1) $frac{du}{dx_1}=5$
2) $frac{du}{dx_1}=5*x_1$
3) $frac{du}{dx_1}=5*x_2$
Can this equations be considered as PDE since in those appears only the derivative with respect a one of the dependent variables?
terminology
asked Jan 18 at 13:45
user2235427user2235427
1083
$endgroup$
$begingroup$
Yes they are. The first equation has solution $5x_1+c$ if u is a function of the single variable $x_1$. It has the solution $5x+f(x_2)$ where f is an arbitrary function of $x_2$ if u depends on $x_1$ and $x_2$.
$endgroup$
– Paul
Jan 18 at 13:49
add a comment |
$begingroup$
From wikipedia: "PDE is a differential equation that contains beforehand unknown multivariable functions and their partial derivatives".
My dubt is: suppose you have the following variable
$u =u(x_1, x_2)$
where $x_1$ and $x_2$ are independent variables
and a particular physical problem that is modeled with one the following equations:
1) $frac{du}{dx_1}=5$
2) $frac{du}{dx_1}=5*x_1$
3) $frac{du}{dx_1}=5*x_2$
Can this equations be considered as PDE since in those appears only the derivative with respect a one of the dependent variables?
terminology
asked Jan 18 at 13:45
user2235427user2235427
1083
$endgroup$
From wikipedia: "PDE is a differential equation that contains beforehand unknown multivariable functions and their partial derivatives".
My dubt is: suppose you have the following variable
$u =u(x_1, x_2)$
where $x_1$ and $x_2$ are independent variables
and a particular physical problem that is modeled with one the following equations:
1) $frac{du}{dx_1}=5$
2) $frac{du}{dx_1}=5*x_1$
3) $frac{du}{dx_1}=5*x_2$
Can this equations be considered as PDE since in those appears only the derivative with respect a one of the dependent variables?
terminology
terminology
asked Jan 18 at 13:45
user2235427user2235427
1083
asked Jan 18 at 13:45
user2235427user2235427
1083
asked Jan 18 at 13:45
user2235427user2235427
1083
asked Jan 18 at 13:45
user2235427user2235427
1083
asked Jan 18 at 13:45
user2235427user2235427
1083
1083
$begingroup$
Yes they are. The first equation has solution $5x_1+c$ if u is a function of the single variable $x_1$. It has the solution $5x+f(x_2)$ where f is an arbitrary function of $x_2$ if u depends on $x_1$ and $x_2$.
$endgroup$
– Paul
Jan 18 at 13:49
add a comment |
$begingroup$
Yes they are. The first equation has solution $5x_1+c$ if u is a function of the single variable $x_1$. It has the solution $5x+f(x_2)$ where f is an arbitrary function of $x_2$ if u depends on $x_1$ and $x_2$.
$endgroup$
– Paul
Jan 18 at 13:49
$begingroup$
Yes they are. The first equation has solution $5x_1+c$ if u is a function of the single variable $x_1$. It has the solution $5x+f(x_2)$ where f is an arbitrary function of $x_2$ if u depends on $x_1$ and $x_2$.
$endgroup$
– Paul
Jan 18 at 13:49
$begingroup$
Yes they are. The first equation has solution $5x_1+c$ if u is a function of the single variable $x_1$. It has the solution $5x+f(x_2)$ where f is an arbitrary function of $x_2$ if u depends on $x_1$ and $x_2$.
$endgroup$
– Paul
Jan 18 at 13:49
add a comment |
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$begingroup$
Yes they are. The first equation has solution $5x_1+c$ if u is a function of the single variable $x_1$. It has the solution $5x+f(x_2)$ where f is an arbitrary function of $x_2$ if u depends on $x_1$ and $x_2$.
$endgroup$
– Paul
Jan 18 at 13:49