# Math Help - Is an exponential solution the correct thing to try here?

1. ## Is an exponential solution the correct thing to try here?

Hi all,

I have an ODE of the form X" + aX' + (bc)^2 X = 0.

Is the correct way of solving this to try an exponential solution of the form Ae^rx?

2. Assuming a,b, and c are constant it could be of this form, have you solved your charateristic equation yet? What did you get?

3. Yes, a,b and c are constants, sorry I forgot to put that in.

It becomes a quadratic equation:

r^2 + ar + (bc)^2 = 0.

The quadratic formula gives

r = [-a + sqrt(a^2 - 4(bc)^2)]/2 and
r = [-a - sqrt(a^2 - 4(bc)^2)]/2.

I note that there will be two independent solutions when the discrimant is positive, that is, when

a^2 - 4(bc)^2 > 0, or

a^2 > 4(bc)^2, or

|a| > |2bc|