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Math Help - Determine the values for r in the differential equation

  1. #1
    Member VitaX's Avatar
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    Determine the values for r in the differential equation

    Determine the value of r for which the given differential equation has solutions of the form y=t^r for t > 0.

    t^2 y'' + 4ty' + 2y = 0

    y'(t) = rt^{r-1}

    y''(t) = r(r-1)t^{r-2}

    t^2[r(r-1)t^{r-2}] + 4t[rt^{r-1}] + 2t^r = 0

    I'm a little confused as how to simplify this down. Can t^2 multiplied by t^{r-2} produce t^r ?
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  2. #2
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    Re: Determine the values for r in the differential equation

    Rules of exponents. Why do you hesitate? Go forth and serve.
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  3. #3
    Member VitaX's Avatar
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    Re: Determine the values for r in the differential equation

    I had forgotten is all, haven't had a math course in a while so I was rusty and for some reason the r constant was throwing me off.
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