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Tough differential equation

  1. Aug 31, 2013 #1
    i tried to solve this question in all the ways i knew but it wouldnt work ..please help

    xy^2dy/dx + y = x^2

    i tried to solve it by using linear first order differential equation technique and also by using different exact and reducable exact differential equaions... help me
     
  2. jcsd
  3. Sep 1, 2013 #2

    Simon Bridge

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    $$xy^2 \frac{dy}{dx} = x^2-y$$
    Rewriting:
    $$\frac{dy}{dx} = \frac{x^2-y}{xy^2} = \frac{x}{y^2}-\frac{1}{xy}$$
    ... hmmmm... what have you tried?
    ... in what context does it show up?
     
  4. Sep 2, 2013 #3
    Hi !

    The ODEs of the kind : dY/dX = f(X)*Y^p + g(X)
    are close to the Bernoulli ODE : dY/dX = f(X)*Y^p + g(X)*Y
    where p is not an integer.
    While we know how to analytically solve the Bernoulli ODE, we don't know to solve dY/dX = f(X)*Y^p + g(X) in the general case.
    The question here is to solve the ODE in the case: p=1/3 , f(x)=-3/2X , g(x)=2/3 (see attachment)
    As far as I know, if g(x)=constant (not 0) the ODE is not analytically solvable.
    So, a numerical method of solving will be required.
     

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