Mathematics for Economists

Calculus of variations

The characteristic equation isλ^2 λ 3 / 4 = 0 .The roots are

λ 1 = 1 / 2 ,λ 2 = 3 / 2 .Thex  8 /3 is a particular solution so the

general solution is

C 1 exp



^1

2

t



+C 2 exp



3

2

t



^8

3

.

Using the boundary conditions

C 1 =

3

e^3 e^1 ,C^2 =

3

e^3 e^1