Hi. If the auxiliary equation of a second order differential equation has 2 complex repeated roots, would I still use: Just in the form: ? Thanks
Last edited by craig; Jun 8th 2009 at 06:38 AM.
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Doesn't matter, found out that you use
Originally Posted by craig Hi. If the auxiliary equation of a second order differential equation has 2 repeated roots, would I still use: Just in the form: ? Thanks If the root is repeated then the general solution is .
Originally Posted by craig Doesn't matter, found out that you use This is the general solution for when the roots are not real, that is, the roots have the form .
Hi thanks for the reply, there was actually a typo in my original post, it was for roots such as . Have fixed the typo now.
Originally Posted by craig Hi thanks for the reply, there was actually a typo in my original post, it was for roots such as . Have fixed the typo now. Assume the coefficients are real. Then the roots come in pairs. I would think the general solution would be for if degree of multiplicity is .
Originally Posted by Sampras Assume the coefficients are real. Then the roots come in pairs. I would think the general solution would be for if degree of multiplicity is . No, that the same as so you have nothing new. For a+ bi a double root of the characteristic equation, you want . That is, multiply the "base" solution by x as mr. fantastic said.
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