Mathematics for Economists

Optimal control, Bolza problem

x=xx( 1 )exp(t+ 1 ),x( 0 )= 1

xx=x( 1 )exp(t+ 1 ),x( 0 )= 1 ,

x e txet=x( 1 )e^2 t+^1

xet=x( 1 )

Z

e^2 t+^1 dt+C=

=x( (^1) )e
2 t+ 1
2

+C,

x(t)=

x( 1 )

2 e

t+ (^1) +Cet