(Solved): 7-1 For the systems described by the following equations, with the input \( x(t) \) and output \( ...

7-1 For the systems described by the following equations, with the input \( x(t) \) and output \( y(t) \), determine which of the systems are linear and which are nonlinear. (a) \( \frac{d y(t)}{d t}+2 y(t)=x^{2}(t) \) (b) \( \frac{d y(t)}{d t}+3 t y(t)=t^{2} x(t) \) (c) \( 3 y(t)+2=x(t) \) (d) \( \frac{d y(t)}{d t}+y^{2}(t)=x(t) \) (e) \( \left(\frac{d y(t)}{d t}\right)^{2}+2 y(t)=x(t) \) (f) \( \frac{d y(t)}{d t}+(\sin t) y(t)=\frac{d x(t)}{d t}+2 x(t) \) (g) \( \frac{d y(t)}{d t}+2 y(t)=x(t) \frac{d x(t)}{d t} \) (h) \( y(t)=\int_{-\infty}^{t} x(\tau) d \tau \)