1is power defined in this case ?
9 Answers
621
i am not very sure at the moment.. but i think 1 ..
My explanation : expansion of ln(dy/dx) will have only powers of dy/dx
degree is the power of the largest term.. which will be d2y/dx2
which is 1 !!!
62yes that is why i said "not very sure"
It is all about definition in some cases...
And different ppl use different definitions...
like some places u will see x is a factor of y if it is not equal to y.. and at some other places this will nto be a requisite!
So in some way we dont need to worry about this question :)
13I also think that the degree should be not defined.
But I want an answer for "why"?
1degree is defined only for differential equations. This is not a differential equation,
A differential equation, by definition, is one in which the differential coeffecients act as the polynomial.
Probably i didn't explain well.
But in this case dy/dx sought of terms will always be a part of some other function like e^x or ln x.
So, degree not defined.
13dy/dx=ln y
is this a diff. eqn. having its degree defined??
33No the basic def of diff equation is...
It is one which connects the independent variable x, unknown or dependent variable f(x) (or say y) and its derivatives(y',y'',y'''.....)
F(x,y,y',y'',y''',y'''',......)=0
they can be dependent by any function....
That polynomial part is only applicable to degree of diff eqn so...
dy/dx=ln y is a diff eqn but its degree is not defined.