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Math Help - picard's method of iteration

  1. #1
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    picard's method of iteration

    Hey guys, I'm having some trouble with this problem using picard's successive approximations:

    y' = 2e^x - y, y(0) = 1

    I thought the equation to begin the approximations would be:

    y = 1 + integral of 2e^x - y

    but when i make the substitution for y it doesn't work... any suggestions????
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  2. #2
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    Quote Originally Posted by collegestudent321 View Post
    Hey guys, I'm having some trouble with this problem using picard's successive approximations:

    y' = 2e^x - y, y(0) = 1

    I thought the equation to begin the approximations would be:

    y = 1 + integral of 2e^x - y

    but when i make the substitution for y it doesn't work... any suggestions????
    Yeah, you're good to go.

     <br />
y_{n+1}(t) = 1 + \int_0^x 2e^t - y_n(t)\,dt\;\;(1)<br />

    Then start with y_0(t) = 1 and use eqn (1) recursively.
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