Mixing
Degree of a differential equation, a paradox
$begingroup$
It is understood that the degree of the differential equation
y"=x^1/5 is 1.
Let it's solution be y(x,c).
Then there is another equation(actually the same)
(y")^5=x
whose solution is same as that for the previous equation.
So if a question is asked that what is the degree of the second differential equation, what will be the answer--1 or 5?
calculus
asked Jan 31 at 6:43
Shubham SinghShubham Singh
1
$endgroup$
add a comment |
$begingroup$
It is understood that the degree of the differential equation
y"=x^1/5 is 1.
Let it's solution be y(x,c).
Then there is another equation(actually the same)
(y")^5=x
whose solution is same as that for the previous equation.
So if a question is asked that what is the degree of the second differential equation, what will be the answer--1 or 5?
calculus
asked Jan 31 at 6:43
Shubham SinghShubham Singh
1
$endgroup$
1
$begingroup$
The degree of both differential equations is $2$. Degree is based on the highest order derivative, which is always an integer value.
$endgroup$
– Hyperion
Jan 31 at 6:48
$begingroup$
You're confusing to definition of degree within polynomials and degree within differential equations.
$endgroup$
– Hyperion
Jan 31 at 6:53
1
$begingroup$
I think with differential equations, I've mostly heard "order", not "degree".
$endgroup$
– Arthur
Jan 31 at 7:21
add a comment |
$begingroup$
It is understood that the degree of the differential equation
y"=x^1/5 is 1.
Let it's solution be y(x,c).
Then there is another equation(actually the same)
(y")^5=x
whose solution is same as that for the previous equation.
So if a question is asked that what is the degree of the second differential equation, what will be the answer--1 or 5?
calculus
asked Jan 31 at 6:43
Shubham SinghShubham Singh
1
$endgroup$
It is understood that the degree of the differential equation
y"=x^1/5 is 1.
Let it's solution be y(x,c).
Then there is another equation(actually the same)
(y")^5=x
whose solution is same as that for the previous equation.
So if a question is asked that what is the degree of the second differential equation, what will be the answer--1 or 5?
calculus
calculus
asked Jan 31 at 6:43
Shubham SinghShubham Singh
1
asked Jan 31 at 6:43
Shubham SinghShubham Singh
1
asked Jan 31 at 6:43
Shubham SinghShubham Singh
1
asked Jan 31 at 6:43
Shubham SinghShubham Singh
1
asked Jan 31 at 6:43
Shubham SinghShubham Singh
1
1
1
$begingroup$
The degree of both differential equations is $2$. Degree is based on the highest order derivative, which is always an integer value.
$endgroup$
– Hyperion
Jan 31 at 6:48
$begingroup$
You're confusing to definition of degree within polynomials and degree within differential equations.
$endgroup$
– Hyperion
Jan 31 at 6:53
1
$begingroup$
I think with differential equations, I've mostly heard "order", not "degree".
$endgroup$
– Arthur
Jan 31 at 7:21
add a comment |
1
$begingroup$
The degree of both differential equations is $2$. Degree is based on the highest order derivative, which is always an integer value.
$endgroup$
– Hyperion
Jan 31 at 6:48
$begingroup$
You're confusing to definition of degree within polynomials and degree within differential equations.
$endgroup$
– Hyperion
Jan 31 at 6:53
1
$begingroup$
I think with differential equations, I've mostly heard "order", not "degree".
$endgroup$
– Arthur
Jan 31 at 7:21
1
1
$begingroup$
The degree of both differential equations is $2$. Degree is based on the highest order derivative, which is always an integer value.
$endgroup$
– Hyperion
Jan 31 at 6:48
$begingroup$
The degree of both differential equations is $2$. Degree is based on the highest order derivative, which is always an integer value.
$endgroup$
– Hyperion
Jan 31 at 6:48
$begingroup$
You're confusing to definition of degree within polynomials and degree within differential equations.
$endgroup$
– Hyperion
Jan 31 at 6:53
$begingroup$
You're confusing to definition of degree within polynomials and degree within differential equations.
$endgroup$
– Hyperion
Jan 31 at 6:53
1
1
$begingroup$
I think with differential equations, I've mostly heard "order", not "degree".
$endgroup$
– Arthur
Jan 31 at 7:21
$begingroup$
I think with differential equations, I've mostly heard "order", not "degree".
$endgroup$
– Arthur
Jan 31 at 7:21
add a comment |
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$begingroup$
The degree of both differential equations is $2$. Degree is based on the highest order derivative, which is always an integer value.
$endgroup$
– Hyperion
Jan 31 at 6:48
$begingroup$
You're confusing to definition of degree within polynomials and degree within differential equations.
$endgroup$
– Hyperion
Jan 31 at 6:53
1
$begingroup$
I think with differential equations, I've mostly heard "order", not "degree".
$endgroup$
– Arthur
Jan 31 at 7:21