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Math Help - second order ODE

  1. #1
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    second order ODE

    Solving v''t + v' = 0

    When I substitute w for v' I get

    \frac{dw}{w}=-\frac{dt}{t}

    ln(t)=-ln(w)+c

    but this gives me w=-t/c \rightarrow w=t/c rather than w=c/t

    A seemingly simple separable equation that I am getting hung up on.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by petition Edgecombe View Post
    Solving v''t + v' = 0

    When I substitute w for v' I get

    \frac{dw}{w}=-\frac{dt}{t}

    ln(t)=-ln(w)+c

    but this gives me w=-t/c \rightarrow w=t/c rather than w=c/t

    A seemingly simple separable equation that I am getting hung up on.
    how did you get that?

    write c as ln(C), then what happens?

    \ln t = - \ln w + \ln C

    but \ln X - \ln Y = \ln (X/Y), so that

    \ln t = \ln (C/w)

    \Rightarrow t = \frac Cw \implies w = \frac Ct
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