√y= dy/dx(x+(√dy/dx))
Degree and order?
#Degree and Order
subtle girder
novel urchinBOT
√y= dy/dx(x+(√dy/dx))
Degree and order?
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haughty bloom
√y= dy/dx(x+(√dy/dx))
Degree and order?
The order of a DE is the order of its highest derivative, while the power of a DE is the highest power of that highest-order derivative (even if derivatives of lower orders have higher powers).
haughty bloom
Wait, square? No.
First, let's determine the order. That should be easy.
What will it be?
subtle girder
2?
haughty bloom
No.
subtle girder
1
haughty bloom
Yes. We have first derivatives, but not second, so order is 1.
As for degree, let's expand the RHS first:
y^(1/2) = y' (x + y'^(1/2))
y^(1/2) = xy' + y'^(3/2)
The order is 1, so look for the highest power of first derivative.
subtle girder
3/2
haughty bloom
Nice!
subtle girder
Okay but here comes the problem
Options are 1,3, 3,1, 3,2, 1,2
Order and degree respectively
Which actually
Confuses me
gritty sandal
The order is 1, so look for the highest power of first derivative.
This is not a very good definition I think
or rather in your terms, the power of a first derivative is ill defined
because two differential equations can be the same
in spite of being written differently
e.g. square both sides, or put them both to the power 3
you get the gist
haughty bloom
or rather in your terms, the power of a first derivative is ill defined
I agree: defining the power of a DE isn't really sensible most of the time. However, that's the definition I've heard of.
The order is the value that's important, anyway.
haughty bloom
Options are 1,3, 3,1, 3,2, 1,2
Oh. Hm... Well, the order is definitely 1.
gritty sandal
I agree: defining the power of a DE isn't really sensible most of the time. Howe...
Yeah, I'm only reacting to this because while I agree with your line of thought, the answer you provided does not match any of the options
So not to criticize you, but just as a gentle reminder that we may be missing some certain criterion
haughty bloom
Yeah, that's true.
subtle girder
So not to criticize you, but just as a gentle reminder that we may be missing so...
What criteria could be missing?
gritty sandal
What criteria could be missing?
I'm currently looking about that
For instance, maybe we need to make sure to write the DE in a certain form?
subtle girder
Perhaps
gritty sandal
like, having a power 1 on y
subtle girder
I tried squaring it but it's futile cause the root is left anyway
gritty sandal
I would not be all too surprised
subtle girder
And I'm not sure how to compute dy/dx{√(dy/dx)}