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Math Help - ODE

  1. #1
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    ODE

    I re posted because i stuffed up the latex code.


    I am stuck on this ODE.

    Boundary conditions are:
    U(0)=U(1)=0

    x^2 * \frac{d^2u}{dx^2} + x * \frac{du}{dx} - 4u = 3x
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  2. #2
    MHF Contributor chisigma's Avatar
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    For the general solution of the 'incomplete' DE...

    x^{2}\cdot \frac{d^{2} u}{du^{2}} + x\cdot \frac{du}{dx} - 4\cdot x =0 (1)

    ... try functions like u(x)= x^{\alpha}.For the particular solution of the 'complete' DE...

    x^{2}\cdot \frac{d^{2} u}{du^{2}} + x\cdot \frac{du}{dx} - 4\cdot x = 3\cdot x (2)

    ... try a function like u(x)= \beta\cdot x...

    Kind regards

    \chi \sigma
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  3. #3
    MHF Contributor

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    Quote Originally Posted by ulysses123 View Post
    I re posted because i stuffed up the latex code.


    I am stuck on this ODE.

    Boundary conditions are:
    U(0)=U(1)=0

    x^2 * \frac{d^2u}{dx^2} + x * \frac{du}{dx} - 4u = 3x
    This is an "Euler-type" or "equipotential" equation. As chisigma said, you can try a solution of the form y= x^\alpha to get the "characteristic equation".

    It is also true that the substitution t= ln(x) converts an "Euler-type" equation into an equation with constant coefficients having the same characteristic equation.
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