Find a such that the solution of y'' + y' − 2y = 0, y(0) = a, y' (0) = 1 tends to zero as t → +∞.

Question

asked Apr 25, 2020 11.7k views

1 Answer

Schpet · Answer 1 · 2020-05-01T05:55:05+0000

Answer:

Explanation:

y'' + y' − 2y = 0, y(0) = a, y' (0) = 1

Auxialary equation is

$m^2+m-2=0\\m=-2,1$

General solution is

y=Ae^(-2x) +Be^x

y(0) = A+B =a

y'(0) = -2Ae^(2x) +Be^x = -2A+B = 1

Eliminate B to get

3A =a-1

We know that y tends to 0 when x tends to infinity for any finite A

i.e. a should be a finite real number.