I need to solve system of two differential delayed equations, but I have some problems. I think that second equation is not mathematicaly correct or possible because of position of time derivatives, can you confirm me that?
$\dfrac{dx}{dt}=b \sin(2 \omega \pi t) + c \cos(2 \omega \pi t) + y(t-\sigma) +dS$
$\dfrac{dy}{dt}=\nu dt + dS(t)$
where dt is time derivative, $\sigma$ is time delay, dS noise. My opinion is that right side of second equation cannot be integrated because of the first term on the right side, what would consist $\nu dt \cdot dt$ what is not usual term in differential equations and I am not sure how we can integrate that, am I right?
Yes, your skepticism is justified. Your equations use an inconsistent notation that does not make sense. I presume that the proper equations are:
$$ \begin{alignat*}{1} \mathrm{d}x &= \big (b \sin(2 \omega \pi t) + c \cos(2 \omega \pi t) + y(t-\sigma)\big) \mathrm{d}t +\mathrm{d}S\\ \mathrm{d}y &= \nu\,\mathrm{d}t + \mathrm{d}S \end{alignat*}$$