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Differential equation

  1. May 8, 2015 #1
    It is a general doubt about the following equation: Imagine I want to calculate an unknown function [tex] y(x)[/tex], and my starting equation is of the type

    [tex] y(x)^{2}=\frac{1}{x^{2}Log^{2}(A(x)y(x)^{2})}[/tex]

    , then, am I allowed to start with the equation

    [tex] y(x)=\frac{1}{xLog(A(x)y(x)^{2})}[/tex]

    and differenciate in both sides of the equation, to obtain a first order diferential equation to get y(x)?

    (Note that the beginning equation is a trascendental equation, but why not trying to solve the first order ODE?)


    Thank you
     
  2. jcsd
  3. May 8, 2015 #2
    I dont see why this wouldn't be allowed but I'd assume setting ##f(x)=y(x)^2## and solving for ##f(x)## would be simpler. You can ofc use ##log(a)^2=log(a)*log(a)=log(2a)## to remove the square on the logarithmic function.
     
  4. May 8, 2015 #3
    Mmm the last property of the logs is not valid. My question actually has to be with the modifications that are allowed on a differential equation. Also, the resulting differential equation using that is not depending on A(g) which annoys me somehow...
     
  5. May 8, 2015 #4
    oh yeah ofc it isnt haha, too late for this here
     
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