Mathematics for Economists

Calculus of variations

First we solve the equation

2 yu(y) d

dy

u(y)+u^2 (y)= 0.

Ifu(y)=0 theny^0 (x)=0 theny(x)is a constant which is not a

solution. We can simplify byu

2 ydu

dy

+u = 0 ,^1

u

du=^1

2 y

dy

lnu = ^1

2

lny+c

u = cp^1

jyj

,y^0 =cp^1

jyj