Differential equation containing convolution

Question

I have to solve a differntial equation that contains a convolution ( for instance $\sin(t)y$). I realize there are two ways of doing that, the first is by Laplace transform and the second is by the direct definition of convolution . My question is how it is possible to solve this equation with Laplace transform without initial conditions (I'm not given the value of the variable function and its derivative at $x=0$). Is there anything like applying an inverse Laplace transform on $y(0)$ , and $y'(0)$? And if I am not understood, just let me know and I'll give a clearer example, it's a home exercise and I don't want you to solve the equation for me, just give me a proper guidance.