The given input signal for 2.7.2 is: x(t) = 3 cos(2 π t) + 6 sin(5 π t).Plz explain steps.Given a causal LTI system described by the differential equation find \(H(s),\) the \(\mathrm\) of \(H(s),\) and the impulse response \(h(t)\) of the system. Classify the system as stable/unstable. List the poles of \(H(s) .\) You should the Matlab residue command for this problem.(a) \(y^{\prime \prime \prime}+3 y^{\prime \prime}+2 y^{\prime}=x^{\prime \prime}+6 x^{\prime}+6 x\)2.7.2 The signal \(x(t)\) in the previous problem is filtered with a continuous-time LTI system having the following frequency response. Find the output \(y(t) .\)2.7.3 Consider the cascade combination of two continuous-time LTI systems.The frequency response of SYS 1 is$$ H_^(\omega)=\left\{\begin 1 & \text { for }|\omega|<6 \pi \\ 0 & \text { for }|\omega| \geq 6 \pi \end\right. $$The frequency response of SYS 2 is$$ H_^(\omega)=\left\{\begin 0 & \text { for }|\omega|<4 \pi \\ 1 & \text { for }|\omega| \geq 4 \pi \end\right. $$(a) Sketch the frequency responses of each of the two systems.(b) If the input signal is