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Math Help - What types of ODE are these?

  1. #1
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    What types of ODE are these?





    The first one I am not sure at all about but is the second one homogenous with a substitution required of ?
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  2. #2
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    Re: What types of ODE are these?

    Quote Originally Posted by Paulo1913 View Post




    The first one I am not sure at all about but is the second one homogenous with a substitution required of ?
    For the first one I guess that there is a typo . Second one is non-exact differential equation so you should apply Integrating Factor Technique :

    Let's denote :

     M=-(x^4+y^4) ~\text{and}~N=xy^3

    \frac{\partial M}{\partial y}=-4y^3 ~ \text{and}~\frac{\partial N}{\partial x}=y^3

    Since :

    \frac{\frac{\partial M}{\partial y}-\frac{\partial N}{\partial x}}{N}=\frac{-5y^3}{xy^3}=\frac{-5}{x}

    Integrating actor is :

     u(x)=e^{-\int \frac{5}{x} \,dx}
    Thanks from Paulo1913
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  3. #3
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    Re: What types of ODE are these?

    Oh I see, thanks. For the first one, it should be a dx for the first term, not another dy.
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