1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential Equation, Change of variables

  1. Jun 16, 2017 #1
    1. The problem statement, all variables and given/known data
    Hi,

    I am looking at this question:

    question.jpg

    With this (part of ) solution:

    solution.jpg

    2. Relevant equations


    3. The attempt at a solution

    I follow up to the last line-

    I do not understand here how we have simply taken the ##1/t^{\alpha m + \alpha}## outside of the derivative ##\frac{\partial}{\partial y} ## since ##y=y(r,t^{\beta}) ## i.e. ##t## and ##y## are not independent variables.... ##\frac{\partial}{\partial t}= \frac{\partial y}{\partial t^{\beta}}\frac{\partial t^{\beta}}{\partial t}##

    Many thanks in advance
     
  2. jcsd
  3. Jun 16, 2017 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    My problems with the algebra start before that.
    A partial derivative expresses the consequences of changing one variable while one or more other variables are held constant. The full notation specifies what is held constant. E.g. if f=f(x,y) then we may write ##\frac {\partial f}{\partial x}\Big\rvert_{y=y_0}##. Nearly always, it is obvious what the 'other' variables are, and we don't need to specify their values, so we omit the vertical bar and its subscript.
    In the present case, I have no idea what is being held constant as y varies.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted