# 2nd order ODE

http://users.on.net/~rohanlal/qM.jpg [Broken]
I don't understand how this answer is obtained for the homogenous solution.
What does characteristic equation in "r" mean and how does it help achieve the final solution of Asin(Wt) + Bcos(Wt)?

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Cyosis
Homework Helper
They use a "guess" solution. They guess that the solution is of the form $e^{rt}$. Plug this "guess" solution into your homogeneous differential equation and you will see how to obtain the characteristic equation.

what does x with two dots mean? why would u guess e^rt, isn't the form of the guess supposed to be the same as the form of the equation?

Cyosis
Homework Helper
Dots are derivatives, two dots is a double derivative. Just plug in the "guess" solution I provided you and show me your work and results.

Define "form of the equation".

Perhaps what the OP means is when you are solving for the nonhomogeneous part, that part of the solution takes the form of the forcing function.

Remember that e^(i*x) = cosx + i*sinx, so e^(i*wt) = ? and e^(i*-wt) = ?

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HallsofIvy