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Math Help - Perturbation Theory help

  1. #1
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    Perturbation Theory help

    Hi...

    The given problem:

    <br />
y\prime-y+\epsilont y^2=0<br />

    Initial condition of y(0) = 1

    And with this I am to compute the first order Pert. Theory Approximation. My question, I'm not sure how to do this with a (t) in the equation. Is it possible or is it a typo?
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  2. #2
    Super Member Rebesques's Avatar
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    Quote Originally Posted by tibetan-knight View Post
    Hi...

    The given problem:

    <br />
y\prime-y+\epsilont y^2=0<br />

    Initial condition of y(0) = 1

    And with this I am to compute the first order Pert. Theory Approximation. My question, I'm not sure how to do this with a (t) in the equation. Is it possible or is it a typo?


    Not really, its ok as long as it tends to zero with the initial value t=0.

    Now, let y_0 solve the initial equation and let y=y_0+\epsilon y_1. By substitution and omitting higher order powers of \epsilon, we get y_1'-y_1=0. Along with y_1(1)=1, we get y=y_0+\epsilon e^{x}.

    Do check my calcs, I am always clumsy on Mondays.
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