Math Problem Solver

Let φ be any solution of 0 ( ) " ' L y = y +a1 y +a2 y = on

an interval I containing a point x0 . Prove that for

all x in I,

0 0 ( ) ( ) ( ) 0 0

k x x k x x x e x x e − − − φ ≤ φ ≤ φ ,

where [ ] 2

1 2 2 φ(x) = φ(x) + φ'(x) ,

k = 1 + a1 + a2 .