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Math Help - help finding the second solution

  1. #1
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    Smile help finding the second solution

    Use reduction of order to find the second solution of the differential equation. Note: Y1 is the first solution.

    x y'' + y' = 0; Y1= lnx


    I know the answer is Y2= 1 but i wonder how they got this, could someone explain me....Please!!!

    Thank you
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  2. #2
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    Quote Originally Posted by kithy View Post
    Use reduction of order to find the second solution of the differential equation. Note: Y1 is the first solution.

    x y'' + y' = 0; Y1= lnx


    I know the answer is Y2= 1 but i wonder how they got this, could someone explain me....Please!!!

    Thank you
    The solution proceeds the same way as in this thread.

    y_2(x) = v(x) \cdot y_1(x)

    Sub this into your differential equation and you will get an equation in the form
    a(x)v'' + b(x)v' = 0
    which you can do a reduction of order on.

    If you are still having troubles after this hint, perhaps you should show us your work so we can better see where you need help.

    -Dan
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