Obtain the Laplace Transform for the following differential equations with the specified initial conditions:
a)
y + 6y' + 13y = 5u(t), y(0) = 1, y'(0) = 4
b)
y + 3y' + 4y = 7u(t), y(1) = 1, y'(1) = 2
c)
y + 3y' + 4y = 6sin(x), y(0) = 4, y'(0) = 5
d)
y + 2y' = u(t), y(0) = 1