Mathematics for Economists

Calculus of variations

Example

Find the extremal

Z 1

0

y

y^0

2

dx,y( 0 )= 1 ,y( 1 )=^3

p

4

The Euler-Lagrange equation is



y^0

2

= (^2) dxd

yy^0

= 2

y^0

2

+ 2 yy^00

2 yy^00 +

y^0

2

= 0.