Mathematics for Economists

Calculus of variations

It is a second order non-linear equation. In this case one can try to

substituteu=y^0 and assume thaty^0 depends onxjust viay.Then

y^00 (x) = dxdy^0 (x)=dxdu(y(x))=dydu(y(x))dxdy(x)

= d

dy

u(y(x))u(y(x)).