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Thread: 1.3.4 verify that the function is a solution of the DE.

  1. #1
    Super Member bigwave's Avatar
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    1.3.4 verify that the function is a solution of the DE.

    1.3.4  verify that the function is a solution of the DE.-13.png
    ok finally number 14
    I assume s means seconds. and we have y, t and s is in this
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    Forum Admin topsquark's Avatar
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    Re: 1.3.4 verify that the function is a solution of the DE.

    Quote Originally Posted by bigwave View Post
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    ok finally number 14
    I assume s means seconds. and we have y, t and s is in this
    Not likely. s and t are more likely just throw away variables. (I've seen them typically used in Laplace transform problems.)

    The difficulty here is taking the derivative of the integral? Just break it into pieces, as always.
    $\displaystyle y = e^{t^2} \int _0^t e^{-s^2}~ds + e^{t^2}$

    $\displaystyle y' = \dfrac{d}{dt} (e^{t^2}) \cdot \int _0^t e^{-s^2}~ds + e^{t^2} \cdot \dfrac{d}{dt} \left ( \int _0^t e^{-s^2}~ds \right ) + \dfrac{d}{dt} (e^{t^2} )$

    Can you do the derivatives?

    -Dan
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