Consider the following differential equation:

$$ t^2 \frac{d^2 y}{d t^2}+7 t \frac{d y}{d t}+8 t y=10 \sin (t) $$

Which one of the following options is correct?

Consider a discrete-time linear time-invariant (LTI) system, $\boldsymbol{S}$, where

$$ y[n]=S\{x(\mathrm{n})\} $$

$$Let\,\,\,\, S\{\delta[n]\}=\left\{\begin{array}{lc} 1, & n \in\{0,1,2\} \\ 0, & \text { otherwise } \end{array}\right. $$

where $\delta[n]$ is the discrete-time unit impulse function. For an input signal $x[n]$, the output $y[n]$ is

Suppose signal $y(t)$ is obtained by the time-reversal of signal $x(t)$, i.e., $y(t) = x(-t)$, $-\infty < t < \infty$. Which one of the following options is always true for the convolution of $x(t)$ and $y(t)$?

Which of the following statement(s) is/are true?