Linear Equations of the Second Kind with Variable Limit of Integration

ABSTRACT

Solution: y(x) = f (x) + λ

eλ(x-t)f (t) dt.

2. y(x) + λx ∫ x

y(t) dt = f (x).

Solution: y(x) = f (x) – λ

x exp [ 1

2λ(t2 – x2) ] f (t) dt.

3. y(x) + λ ∫ x

ty(t) dt = f (x).

Solution: y(x) = f (x) – λ

t exp [ 1

2λ(t2 – x2) ] f (t) dt.