My try:

I applied Laplace transform on both sides of the equation.

$sL\{y(t)\}=\frac{1}{{s}^{2}+1}+L\{cos(t)\ast y(t)\}\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}sL\{y(t)\}=\frac{1}{{s}^{2}+1}+L\{cos(t)\}\times L\{y(t)\}$

Now, I'm stuck on applying the inverse Laplace transform on (*) to find $y(t)$