If all roots of the polynomial...
... have real part , then if is solution of the second order DE you have prosed is...
a,b,c > 0
ay'' + by' +cy = 0
and y(0) = c and y'(0) = d
the equation has either one real root, two real roots or two complex roots, but how do i then show that in the limit x--> +infinity, y(x) will go to zero?
Appreciate Your help!
A polynomial whose roots have all real part is called 'Hurwitz polynomial'. If we write a polynomial of degree n in t as and it is , necessary [but not sufficient...] condition for to be Hurwitz is that . For a suffcient condition see...
Hurwitz polynomial - Wikipedia, the free encyclopedia