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Math Help - degree of differential equation

  1. #1
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    degree of differential equation

    what can be degree of differential equation e^{\frac{dy}{dx}}=2
    my working
    if I expand e^twhere t={\frac{dy}{dx}} then degree seems to be not defined as tgoes up to infinity but if i take ln(natural log)on both sides then degree seems to be 1
    as we get {\frac{dy}{dx}}=ln2 where is the problem ? is modification changed the equation in other form[/quote]
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  2. #2
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    Re: degree of differential equation

    Yes, that is a first order differential equation.

    Even in the first form, [itex]e^{dy/dx}= 2[/itex] there is only a first order derivative.

    Even if you expand in a power series:
    1+ \frac{dy}{dx}+ \frac{1}{2!}\left(\frac{dy}{dx}\right)^2+ \frac{1}{3!}\left(\frac{dy}{dx}\right)^3+ \cdot\cdot\cdot
    You have only the first derivative! The powers of that first derivative give the degree not the order- it is still first order.
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  3. #3
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    Re: degree of differential equation

    Quote Originally Posted by HallsofIvy View Post
    Yes, that is a first order differential equation.

    Even in the first form, [itex]e^{dy/dx}= 2[/itex] there is only a first order derivative.

    Even if you expand in a power series:
    1+ \frac{dy}{dx}+ \frac{1}{2!}\left(\frac{dy}{dx}\right)^2+ \frac{1}{3!}\left(\frac{dy}{dx}\right)^3+ \cdot\cdot\cdot
    You have only the first derivative! The powers of that first derivative give the degree not the order- it is still first order.
    sir I am taking about degree according to our book degree and order are two different terminology.sir see this General Terms of Ordinary Differential Equations
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  4. #4
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    Re: degree of differential equation

    ir i am confused in order and degree as given in link above .please clear my doubt
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