# Thread: Homog. Lin. Eq's with Constant Coeff.

1. ## Homog. Lin. Eq's with Constant Coeff.

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

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

WORK:

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

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:

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

Is this right?

2. Originally Posted by Ideasman
Find the general sol'n of the given Dif EQ:

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

WORK:

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

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:

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

Is this right?
That is OK for the equation you are working on, but its not the equation you
are asked to solve, which has a double root.

RonL

3. Originally Posted by CaptainBlack
That is OK for the equation you are working on, but its not the equation you
are asked to solve, which has a double root.

RonL
Ha, think I copied down the wrong one on here:

It should have been $8y'' + 2y' - y = 0$. Ok, so it's right if it was that ?

4. Originally Posted by Ideasman
Ha, think I copied down the wrong one on here:

It should have been $8y'' + 2y' - y = 0$. Ok, so it's right if it was that ?
Yes

RonL