Hi 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.