determine the value of P in higher order

[chohahur]

hi, I am confused about finding the p value somehow in the higher order equations. is the p supposed to be the coefficient of the second term, or the coefficient of the second highest term?

 for example, if we have an equation y''' - 10y' +6y = 5e^(-9t), is the p value suppose to be -10 or what? thanks

[Amanda-fazi]

according to the Abel rule, the value of p is always going to be the coefficient of (n-1)th derivative term(as n=>the highest time of derivative , under the assumption that the coefficient of the highest term =1. while the coefficient of the second term is not important.

in this question, we can see the equation as y''' - 0y'' + 10y' +6y = 5e^(-9t), therefore the value of p = 0 from 0y''.