Differential Equation linear, separable, neither or both?
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I am stuck on deciding whether or not the differential equation
$$frac{dy}{dx} = frac{1}{x} + frac{1}{y}$$ is linear or separable? I believe it is linear although I am confused on the value of $P(x)$ since $frac{1}{y} < y$.
Any help would be appreciated
calculus differential-equations
edited Nov 15 at 23:17
the_candyman
8,55921944
asked Nov 15 at 23:15
ilovesports524
21
add a comment |
up vote
0
down vote
favorite
I am stuck on deciding whether or not the differential equation
$$frac{dy}{dx} = frac{1}{x} + frac{1}{y}$$ is linear or separable? I believe it is linear although I am confused on the value of $P(x)$ since $frac{1}{y} < y$.
Any help would be appreciated
calculus differential-equations
edited Nov 15 at 23:17
the_candyman
8,55921944
asked Nov 15 at 23:15
ilovesports524
21
What is $P(x)$?
– the_candyman
Nov 15 at 23:28
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am stuck on deciding whether or not the differential equation
$$frac{dy}{dx} = frac{1}{x} + frac{1}{y}$$ is linear or separable? I believe it is linear although I am confused on the value of $P(x)$ since $frac{1}{y} < y$.
Any help would be appreciated
calculus differential-equations
edited Nov 15 at 23:17
the_candyman
8,55921944
asked Nov 15 at 23:15
ilovesports524
21
I am stuck on deciding whether or not the differential equation
$$frac{dy}{dx} = frac{1}{x} + frac{1}{y}$$ is linear or separable? I believe it is linear although I am confused on the value of $P(x)$ since $frac{1}{y} < y$.
Any help would be appreciated
calculus differential-equations
calculus differential-equations
edited Nov 15 at 23:17
the_candyman
8,55921944
asked Nov 15 at 23:15
ilovesports524
21
edited Nov 15 at 23:17
the_candyman
8,55921944
asked Nov 15 at 23:15
ilovesports524
21
edited Nov 15 at 23:17
the_candyman
8,55921944
edited Nov 15 at 23:17
the_candyman
8,55921944
edited Nov 15 at 23:17
the_candyman
8,55921944
8,55921944
asked Nov 15 at 23:15
ilovesports524
21
asked Nov 15 at 23:15
ilovesports524
21
asked Nov 15 at 23:15
ilovesports524
21
21
What is $P(x)$?
– the_candyman
Nov 15 at 23:28
add a comment |
What is $P(x)$?
– the_candyman
Nov 15 at 23:28
What is $P(x)$?
– the_candyman
Nov 15 at 23:28
What is $P(x)$?
– the_candyman
Nov 15 at 23:28
add a comment |
2 Answers
2
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0
down vote
For sure, it is not linear. Check this link to understand the meaning of linearity.
Moreover, it is not separable, since you can not rewrite it as:
$$frac{dy}{dx} = f(y)g(x).$$
In fact:
$$frac{1}{x} + frac{1}{y} = frac{x+y}{xy} neq f(y)g(x).$$
answered Nov 15 at 23:26
the_candyman
8,55921944
add a comment |
up vote
0
down vote
The standard form of a first order linear differential equation in $(y,x)$ is given as ,
$frac{dy}{dx}+P(x)y=Q(x)$.
Since your equation cannot be written as above equation.
So your equation is not linear in $(y,x)$.
Hence $P(x)$ does not exist.
As @the_candyman showed that it is not a separable too.
answered Nov 16 at 11:39
Sachin Kumar
20518
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
For sure, it is not linear. Check this link to understand the meaning of linearity.
Moreover, it is not separable, since you can not rewrite it as:
$$frac{dy}{dx} = f(y)g(x).$$
In fact:
$$frac{1}{x} + frac{1}{y} = frac{x+y}{xy} neq f(y)g(x).$$
answered Nov 15 at 23:26
the_candyman
8,55921944
add a comment |
up vote
0
down vote
For sure, it is not linear. Check this link to understand the meaning of linearity.
Moreover, it is not separable, since you can not rewrite it as:
$$frac{dy}{dx} = f(y)g(x).$$
In fact:
$$frac{1}{x} + frac{1}{y} = frac{x+y}{xy} neq f(y)g(x).$$
answered Nov 15 at 23:26
the_candyman
8,55921944
add a comment |
up vote
0
down vote
up vote
0
down vote
For sure, it is not linear. Check this link to understand the meaning of linearity.
Moreover, it is not separable, since you can not rewrite it as:
$$frac{dy}{dx} = f(y)g(x).$$
In fact:
$$frac{1}{x} + frac{1}{y} = frac{x+y}{xy} neq f(y)g(x).$$
answered Nov 15 at 23:26
the_candyman
8,55921944
For sure, it is not linear. Check this link to understand the meaning of linearity.
Moreover, it is not separable, since you can not rewrite it as:
$$frac{dy}{dx} = f(y)g(x).$$
In fact:
$$frac{1}{x} + frac{1}{y} = frac{x+y}{xy} neq f(y)g(x).$$
answered Nov 15 at 23:26
the_candyman
8,55921944
answered Nov 15 at 23:26
the_candyman
8,55921944
answered Nov 15 at 23:26
the_candyman
8,55921944
answered Nov 15 at 23:26
the_candyman
8,55921944
8,55921944
add a comment |
add a comment |
up vote
0
down vote
The standard form of a first order linear differential equation in $(y,x)$ is given as ,
$frac{dy}{dx}+P(x)y=Q(x)$.
Since your equation cannot be written as above equation.
So your equation is not linear in $(y,x)$.
Hence $P(x)$ does not exist.
As @the_candyman showed that it is not a separable too.
answered Nov 16 at 11:39
Sachin Kumar
20518
add a comment |
up vote
0
down vote
The standard form of a first order linear differential equation in $(y,x)$ is given as ,
$frac{dy}{dx}+P(x)y=Q(x)$.
Since your equation cannot be written as above equation.
So your equation is not linear in $(y,x)$.
Hence $P(x)$ does not exist.
As @the_candyman showed that it is not a separable too.
answered Nov 16 at 11:39
Sachin Kumar
20518
add a comment |
up vote
0
down vote
up vote
0
down vote
The standard form of a first order linear differential equation in $(y,x)$ is given as ,
$frac{dy}{dx}+P(x)y=Q(x)$.
Since your equation cannot be written as above equation.
So your equation is not linear in $(y,x)$.
Hence $P(x)$ does not exist.
As @the_candyman showed that it is not a separable too.
answered Nov 16 at 11:39
Sachin Kumar
20518
The standard form of a first order linear differential equation in $(y,x)$ is given as ,
$frac{dy}{dx}+P(x)y=Q(x)$.
Since your equation cannot be written as above equation.
So your equation is not linear in $(y,x)$.
Hence $P(x)$ does not exist.
As @the_candyman showed that it is not a separable too.
answered Nov 16 at 11:39
Sachin Kumar
20518
answered Nov 16 at 11:39
Sachin Kumar
20518
answered Nov 16 at 11:39
Sachin Kumar
20518
answered Nov 16 at 11:39
Sachin Kumar
20518
20518
add a comment |
add a comment |
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What is $P(x)$?
– the_candyman
Nov 15 at 23:28