help finding the second solution

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• Jun 24th 2008, 08:51 PM
kithy
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
• Jun 25th 2008, 03:53 AM
topsquark
Quote:

Originally Posted by kithy
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.

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

Sub this into your differential equation and you will get an equation in the form
$\displaystyle a(x)v'' + b(x)v' = 0$
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