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I have a question for change of notation.

Quote from text book:

As an example of a singular problem on a finite interval, consider the equation

xy'' + y' + λxy = 0, (6)

or

−(xy')' = λxy, (7)

on the interval 0 < x < 1, and suppose that λ > 0. This equation arises in the study of

free vibrations of a circular elastic membrane, and is discussed further in Section 11.5.

If we introduce the new independent variable t defined by t =sqrt(λ)x, then

dy/dx=sqrt(λ)*dy/dt,

d2y/dx2 = λ*d2y/dt2.

...

my question is the steps involved in deriving d2y/dx2 = λ d2y/dt2.

My understanding in deriving dy/dx=sqrt(λ)*dy/dt is as follows:

since dy/dt = dy/dx*dx/dt

and dx/dt ->(using differentials) dt = sqrt(λ)dx -> dx/dt = 1/sqrt(λ) -> dy/dx = sqrt(λ)*dy/dt.

However, how do you derive d2y/dx2 = λ d2y/dt2?

I get 1=1 which is no help at all?

Sorry if this is noobie, I'm kind of new.

Also, is there a online notepad for practicing mathjax synatax? I like pretty equations.

Thank you.

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# Change of variable for leibniz notation

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