Take the Laplace transform of the IVP

Question

-4 dy/dt - y = 0 y(0) = -8

I need to use Y for laplace transform of y

( ) = Y{0}

So Y = ( ) / (s - )

and y(t) = -8e^(-t/4)

Answer 1

dy/dt + 1/4y = 0; y(0) = - 8;

sY(s) + 8 + 1/4Y(s) = 0; Y(s) = - 8(s + 1/4); y(t) = L^-1[- 8/(s + 1/4)] = - 8e^-t/4