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**Ideasman** 3.) Solve the following Dif EQ, given the indicated initial conditions:

$\displaystyle \frac{d^4y}{dt^4} - y = 0$, $\displaystyle y(0) = y'(0) = y''(0) = 0, y'''(0) = 1$

Okay, my second attempt.. I def. messed up the first time.

The auxiliary equation is m^4 - 1 = 0.

We get: $\displaystyle (m - 1)*(m + 1)*(m^2 + 1) = 0$

Thus, $\displaystyle m = 1, -1 , i, -i$

So, $\displaystyle y = c_1e^t + c_2e^(-t) + c_3e^t(sin(x) + c_4e^tcos(x)$

**Is this right?** I think it is. So, if this is right, then I can find [tex]y', y'', y''' and solve the equations. However, wouldn't it be hard trying to solve the equations for $\displaystyle c_1, c_2, c_3, c_4$... it just feels as there is too much unknown..