You have not understood the definition.
The first term requires y(0), whci is zero. It is therefore not a non-zero term.
The second term is related to 8*sin(0) + 7*e^(0) = 7 -- This should lead you to the first non-zero term.
The third term whould be related to y".
You need values of the function and its derivatives. When they give you a derivative, don't be afraid of it.