I know this is an simple problem but for the life of me Im lost. I am confused on the second order deriv I dont know how to handle it.

Verify that y is a solution of the differential equation.

$\displaystyle y = e^-2x; y'' + y' -2y = 0$

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- Jul 12th 2008, 08:10 AMvodkaDifferential Equation Help!
I know this is an simple problem but for the life of me Im lost. I am confused on the second order deriv I dont know how to handle it.

Verify that y is a solution of the differential equation.

$\displaystyle y = e^-2x; y'' + y' -2y = 0$ - Jul 12th 2008, 08:23 AMtopsquark
$\displaystyle y = e^{-2x}$

$\displaystyle y' = -2e^{-2x}$

$\displaystyle y'' = 4e^{-2x}$

Now just sub into the differential equation and verify that the left hand side is 0.

You could even do it like this:

$\displaystyle y' = -2y$

$\displaystyle y'' = 4y$

So

$\displaystyle y'' + y' -2y = 0$

$\displaystyle 4y - 2y - 2y = 0$

-Dan - Jul 12th 2008, 08:26 AMvodka