Question

laplace dy/dx +4y=1

Answer 1

Any initial conditions given?

Answer 2

This table might help- http://www.intmath.com/laplace-transformation/table-laplace-transforms.php

Answer 3

dy/dx +4y=1

sY - f(0) + 4Y = 1/s
Make Y as subject. When take inverse of it. You should be able to solve the DE.