Quick question on repeated roots when solving differential equations

vendredi 30 mai 2014

say we have gone through the steps and have...



##(\lambda - 2)^{2}(\lambda ^{2}-9) = 0##



which we can write as...



##(\lambda - 2)(\lambda - 2)(\lambda ^{2}-9) = 0##



we have value for lambda of 2, 2, 3, -3



because we have a repeated root.



now, say we have



##(\lambda^{2} - 1)(\lambda + 1) = 0##



my question is would you have 2 values of -1 like the example above i.e. 1, -1, -1? or would you have values of lambda of just 1, -1? and if the former would you treat the -1 as a repeated root?



it becomes important when writing the solution because for a repeated root there an x in the second term with the exponential.



thanks in advance for any direction on this.





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