(Solved): need help woth all questions Q1. For the systems described by the following equations, with the inpu ...

Q1. 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- Jusity your answer. (04 points) (i) $$\frac{dy(t)}{dt}+2y(t)=x^2(t)$$ (ii) $$\frac{dy(t)}{dt}+3ty(t)=t^{2}x(t)$$ (iii) $$3y(t)+2=\mathrm{x}(t)$$ (iv) $$\frac{dy(t)}{dt}+y^2(\mathrm{t})=\mathrm{x}(t)$$ Q2. For the systems described by the following equations, with the input $$x(t)$$ and output $$y(t)$$, determine which are causal and which are noncausal. ( 04 points) (i) $$y(t)=\mathrm{x}(t?2)$$ (ii) $$y(t)=x(?t)$$ (iii) $$y(t)=\mathrm{x}($$ at $$)a>1$$ (iv) $$y(t)=\mathrm{x}($$ at $$)a<1$$ Q3. For the systems described by the following equations, with the input $$x(t)$$ and output $$y(t)$$, explain with reasons which of the systems are time-invariant parameter systems and which are time-varyingparameter systems. (04 points) (a) $$y(t)=x(t?2)$$ (b) $$y(t)=x(?t)$$ (c) $$y(t)=x(at)$$ (d) $$y(t)=tx(t?2)$$ Q4. For the circuit depicted in the following figure, find the differential equations relating outputs $$y1(t)$$ and $$y_2(t)$$ to the input $$x(t)$$. (03 points)