linearity

Consider the following differential equation: $t^2 \frac{d^2y}{dt^2} + 7t \frac{dy}{dt} + 8ty = 10 \sin(t)$ Which one of the following options is correct?

The input $x(t)$ and the output $y(t)$ of a system are related as $y(t) = e^{-t} \int_{-\infty}^{t} e^{\tau} x(\tau) d\tau, \quad -\infty < t < \infty$. The system is

The input $x(t)$ and the output $y(t)$ of a system are related as $$ y(t) = e^{-t} \int\limits_{-\infty}^{t} e^{\tau} x(\tau) d\tau, \quad - \infty The system is

Which of the following differential equations is/are nonlinear?

If the input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\max [0, x(t)]$, then the system is

Consider a continuous-time system with input x(t) and output y(t) given by $$y\left(t\right)=x\left(t\right)\cos\left(t\right)$$. This system is

The system represented by the input-output relationship $$y\left(t\right)=\int_{-\infty}^{5t}x\left(\tau\right)d\tau$$, t > 0 is