Calculus of variations
0 =ψ^0 ( 0 )=φ^0 a(x(a))y(a)+φ^0 b(x(b))y(b)+
Zb
a
Fx^0 y+Fx^0 y dt.
Again integrating by parts
Zb
a
Fx^0 y dt =
h
Fx^0 y
ib
a
0 =ψ^0 ( 0 )=φ^0 a(x(a))y(a)+φ^0 b(x(b))y(b)+
Zb
a
Fx^0 y+Fx^0 y dt.
Again integrating by parts
Zb
a
Fx^0 y dt =
h
Fx^0 y
ib
a