Question

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

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