1. ## Differential 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.

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

2. Originally Posted by vodka
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.

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

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

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

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

3. Originally Posted by topsquark
$\displaystyle y = e^{-2x}$

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

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

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
Duh thanks im an idiot its been awhile since I looked over these.

Cheers Dan