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Math Help - Help with simplifying a 2nd order pde

  1. #1
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    Help with simplifying a 2nd order pde

    I have been given the equation:

    dp/dt = 4 + 1/e*(d/de(e*dp/de))

    the d's are partial derivatives

    I am trying to solve for p. i am told to make the assumtion that the equations are separable and then convert the equation into a ordinary differential equation.

    What i have done so far:
    Set the RHS = 0 4 + 1/e*(d/de(e*dp/de)) = 0
    use chain rule: 4 + 1/e*dp/de + d/de(dp/de)

    is what i have done correct????????
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  2. #2
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    Re: Help with simplifying a 2nd order pde

    There's a couple of things you can do here! First, assume solutions in the form

    p = T(t) + E(e).

    This gives

    T' = 4 + E'' + \frac{E'}{e}.

    This then implies that T = (a+4)t + b leaving the ODE

    E'' + \frac{E'}{e} = a.

    Second, let p = 4t + P. This reduces your PDE to

    P_t = P_{ee} + \frac{P_e}{e}.

    Then assume solutions of the form P = T(t) E(e) and you will get two ODEs for T and E.
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