Match each of the items $$A, B, C$$ with an appropriate item from $$1, 2, 3, 4$$ and $$5$$

List-$${\rm I}$$
$$(P)$$ $${a_1}{{{d^2}y} \over {d{x^2}}} + {a_2}y{{dy} \over {dx}} + {a_3}y = {a_4}$$
$$(Q)$$ $${a_1}{{{d^2}y} \over {d{x^3}}} + {a_2}y = {a_3}$$
$$(Q)$$ $${a_1}{{{d^2}y} \over {d{x^2}}} + {a_2}x{{dy} \over {dx}} + {a_3}{x^2}y = 0$$

List-$${\rm II}$$
$$(1)$$ Non-linear differential equation
$$(2)$$ Linear differential equation with constants coefficients
$$(3)$$ Linear homogeneous differential equation
$$(4)$$ Non-linear homogeneous differential equation
$$(5)$$ Non-linear first order differential equation

Write down the sequence of Instructions which are actually (till HLT instruction), if the program begins with the location 1FF5H.

The circuit shown in the figure, is initially in its steady state. Switch is opened at t = 0.
(1) Determine the initial voltage, V_C(0^-), across the capacitor, and the initial current, i_L(0^-) , through the indicator.
(2) Calculate the voltage, V_L(t) , across the inductance for t > 0.

Assuming that the amplifier shown in the Fig., below, is a voltage-controlled voltage source, show that the voltage transfer function of the network is given by
$$T(s) = {{{V_2}\,(s)} \over {{V_1}\,(s)}} = \,{K \over {{s^2} + \,(3 - K)\,s + 1}}$$