Take the Laplace transform of the IVP -4 dy/dt - y = 0 y(0) = -8

Question

Take the Laplace transform of the IVP

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

I need to use Y for laplace transform of y

( ) = Y{0}

So Y = (-8) / (s - 1/4 )

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

I tried sY+8+1/4Y = Y{0} but it says I am incorrect, I also tried the bold part and that is incorrect.

I also tried this

dy/dt + 1/4y = 0;

sY(s) + 8 + 1/4Y(s) = 0; Y(s) = - 8/(s + 1/4);

y(t) = L^-1(- 8/(s + 1/4) = - 8e^{- t/4}

Answer 1

dy/dt + 1/4y = 0;

sY(s) + 8 + 1/4Y(s) = 0; Y(s) = - 8/(s + 1/4);

y(t) = L^-1(- 8/(s + 1/4) = - 8e^{- t/4}