Find the general sol'n of the given Dif EQ:

$\displaystyle 1.) \frac{d^2y}{dt^2} - 10\frac{dy}{dt} + 25y = 0$

WORK:

$\displaystyle 8y'' + 2y' - y = 0$

So our auxiliary eq. is 8m^2 + 2m - 1 = 0

Factor: (2m + 1)(4m - 1) = 0,

So m = -1/2, 1/4.

Therefore, the gen. sol'n is:

$\displaystyle y = c_1e^{\frac{-t}{2}} + c_2e^{\frac{t}{4}}$

Is this right?